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Answers
Answer:
y = (1/4) 2^x
Step-by-step explanation:
Remark
y = a * x^n is the general equation. Let's see what that means.
Solution
Solve for x
t_12 = a x^12
1024 = a x^12
t_8 = a x^8
64 = a x^8
Now divide the two equations.
1024/64 = a x^12/a x^8 Cancel out the as
1024 / 64 = x^12 / x^8
16 = x^(12 - 8)
16 = x^4 Take the 4th root of both sides.
[tex]\sqrt[4]{x^4}[/tex] = [tex]\sqrt[4]{16}[/tex]
x = 2
Go back and solve for a
y_12 = a x^12
1024 = a 2^12
1024 = a 4096 Divide by 4096
1024 / 4096 = a
a = 1/4
Problem 7
a) First of negative numbers are probably not a good idea. It means that the population is going to decrease. That's not what will happen if you take care of the fruit flies.
So for the domain, 0 is a good starting point.
That will give you 100 flies on day 0. That's how many you bought.
I'm not a biologist so I have no idea in the world how long a fruit fly will live even with the best of care. I'm going to try 60 days and see what happens.
y = 100 * 1.05 ^60
y = 100 * 18.68
y = 1868
Is this number reasonable? Even with the biggest olive jar you can find, and the best care, I don't think that number is realistic. It's too large. Eventually all will die of disease because they are living in their own waste. So Let's try 20 days
y = 100 * 1.05^20
y = 100 * 2.65
y = 265
That's a lot more reasonable. So for convenience sake let us say that 265 flies could live for 20 days
So to answer the question
The domain would be 0 to 20
The range would be 100 to 265
b)
2 weeks = 2*7 days
2 weeks = 14 days
y = 100 * 1.05^14
y = 100 * 1.98
y = 198 fruit flies.
Related Questions
what duos e=mc² mean
Answers
Answer:
energy equals mass times the speed of light squared
Step-by-step explanation:
explanation : Albert Einstein was the one who made that!
A group of football is formed a circle in the middle of the field to stretch out. The circle had a diameter of 30 yards. which measurement is close to the circumference of the circle in yards?
Answers
Answer: Solution
A=πr2=π·302≈2827.43339
Step-by-step explanation:
(111)-8,5
3.
Write the following integers in ascending order (smallest to biggest).
Do you
(i) -5,2,1,-8
(ii) -4,-3, -5,2
(iii) -10,-15,-7
Answers
Answer:
(I) -8, -5, 1, 2
(ii) -5, -4, -3, 2
(iii) -15, -10, -7
Step-by-step explanation:
You can think about what a number line looks like to solve problems like this, for example a number line that goes from -10 to 10 would look something like this, with smaller numbers on the left and bigger on the right
-10, -9, -8, -7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10
A piece of paper has an area of 93.5 square inches. How many times does it need to be folded in half before the area is less than 1 square inch? Explain how you know.
Answers
Answer:
7 times.
Step-by-step explanation:
Keep dividing 93.5 by 2 until it becomes less than 1.
The sheet needs to be folded in half 7 times.
Since the area of the piece of paper is 93.5 square inches, and we need to fold the sheet in half it 'n' times to get an area less than 1 square inch. This is written mathematically as 93.5(1/2)ⁿ ≤ 1.
So, dividing through by 93.5, we have
(1/2)ⁿ ≤ 1/93.5
(1/2)ⁿ ≤ 0.0107
taking natural logarithm of both sides, we have
㏑(1/2)ⁿ ≤ ㏑0.0107
n㏑(1/2) ≤ ㏑(0.0107)
n ≤ ㏑(0.0107)/㏑(1/2)
n ≤ -4.538/-0.693
n ≤ 6.55
Rounding up to the nearest whole number,
n ≅ 7
So, the sheet needs to be folded in half 7 times.
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Miss Landry is getting married soon. She would like to hire a professional who will come to her house and do hair and makeup for the bridal party on her wedding day. She has narrowed it down to two possible choices. A woman from Springdale Salon charges an initial fee of $40 and then an additional $15 per hour. Alternatively, a team from Beauty by Dan offers a free consultation and then charges a higher hourly rate of $35. If it takes a certain amount of time to finish everyone's hair and makeup, Miss Landry will end up paying the same amount either way. How much would Miss Landry end up paying?
Answers
40+15=55+15=70(2 hours )
35+35=70(2 hours)
State weather ABC and AED are congruent. Justify your answer
Answers
I think the answer is c. I hope this helps. Be safe out there!
Bert wants to save $5,742 so that he can buy the car he wants. If Bert can save $18 per day, how many days will it take him to save enough money?
Answers
Answer:
319 days
Step-by-step explanation:
5742/18=319 days
Farmer brown uses super dip to ensure his cattles are free of parasites. What is the independent variable when cattles are devided into three groups?
Answers
Answer:
what are there any numbers
Step-by-step explanation:
HELP HOW DO I FIND THE VALUE OF X
Answers
9514 1404 393
Answer:
7. 118
8. 27
Step-by-step explanation:
Make use of the fact that the sum of angles in a triangle is always 180°.
__
7. 33 + 29 + x = 180 . . . . . numbers in degrees
x = 180 -62 . . . . . . . . . . . subtract 62 from both sides of the equation
x = 118
__
8. 21 +x + 132 = 180
x = 180 -153 . . . . . . . subtract 153
x = 27
Two number cubes are tossed. Find P(1, then 2 or 3).
Answers
Answer:
1/2
Step-by-step explanation:
Answer:
1/6 × 2/6 × 3/6 = 1/36
Step-by-step explanation:
All changes saved
Shane invested $3,500 in a savings account that pays 4% interest semiannually (every 6 months). How much
money will he have in his account in 5 years?
Answers
Answer:
$4,266.48
Step-by-step explanation:
Hope this helps.
Cranberry juice is made with a 16:3:1 ratio of water:sugar:cranberries. How much water,
in gallons, how much water is needed in order to make three gallons of cranberry juice? Express your answer as a
common fraction.
Answers
Answer:
2 2/5
Step-by-step explanation:
We need to find out how many gallons of water so,
16/20 = water
3 gallons * 16/20 = 48/20 = 2 8/20 = 2 2/5
this works because then cranberries would be:
2 2/5/16 = 15/100
and for sugar that means
15/100 * 3 = 45/100
so in total
2 40/100 + 45/100 + 15/100 = 3 gallons
and if we simpilfy 2 40/200 we get 2 2/5
a bottle of orange juice holds for 4/6 quarts of juice. a bottle of pineapple juice holds 2/3 quarts of juice. which bottle has more juice
Answers
Answer:
the orange juice has more ounces than the pineepple juice
Step-by-step explanation:
Suppose a student carryinga virus returns toan isolated college campus o 1000 students. Determine a differential equation for the number x(t) who have contracted the fluif the rate at which the disease spreads is proportional to the number of interactions between the number of students who have the fluand the number of students show have not been exposed to it.
Answers
Answer:
[tex]\frac{dx}{dt}[/tex] = k.x.[1000 - x] ;
where k is the proportionality constant
Step-by-step explanation:
Let
The number of people who are infected with the flu = x(t)
Total number of students = 1000
So,
Total number of student who do not expose with the flue = 1000 - x(t)
As given,
We have to find the differential equation such that
The rate at which the disease spreads is proportional to the number of interactions between the number of students who have the flu and the number of students show have not been exposed to it.
⇒[tex]\frac{dx}{dt}[/tex] ∝ x(t) . [ 1000 - x(t) ]
⇒[tex]\frac{dx}{dt}[/tex] = k.x.[1000 - x] ; where k is the proportionality constant
at a school there are 10 students taking only chemistry, 9 students taking only physics 5 students taking both, and 16 students not taking either. if a student is randomly selected from the other school, what is the probability that they are taking chemistry or physics?
Answers
Answer:
24/16 (not simplified nor teacher checked)
Step-by-step explanation:
What you would need to do is add up all of the students that are taking chemistry, physics, or both. Then place that number in a divsion form.
10+9= 19+5=24
16
24/16
Answer:
[tex]\frac{3}{5}[/tex]
Step-by-step explanation:
the graph shows how many saketboards a company made over a period of time.How can you show that the slope is constant
Answers
Do you have a picture of the graph because we need to know how many skateboards.
A car travels 136 miles using 7 gallons of gas. At that rate, how far can the car travel using 42 gallons of gas?
Answers
Answer:
in 136 miles=7 gallons
?=42 gallon
= 136=7
?=42
cross multiply
136×42=5,712
=5,712÷7=816
Answer:
816 miles
Step-by-step explanation:
136miles/7 g =19.43
19.43 x 42 ≅ 816.06
or
136/7 = X/42
solve for X
42/7 =6, then 136 x6= 816
x = 816 miles
4x + 5y = 48
Y=3x + 2
Answers
4x + 15x + 10 = 48
19x + 10 = 48
19x = 38
x = 2
y = 3x + 2
y = 3(2) + 2
y = 6 + 2
y = 8
The solution of the given equation is x = 2 and y = 8.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
The value of x and y will be calculated as,
4x + 5(3x+2) = 48
4x + 15x + 10 = 48
19x + 10 = 48
19x = 38
x = 2
Calculate the value of y,
y = 3x + 2
y = 3(2) + 2
y = 6 + 2
y = 8
Therefore, the solution of the given equation is x = 2 and y = 8.
To know more about an expression follow
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please answer it’s urgent!!
Answers
Perimeter = 16
Perimeter = 32
Area = length x width so 8 x 8 = 64
Perimeter = ALL sides ADDED up together so 8 + 8 + 8 + 8 = 32
if the length of a box is 17 cm breadth is 6 cm and volume is 1020 cube find the height of the box
Answers
Answer:
10 cm
Step-by-step explanation:
17×6×h=1020
102h=1020
h=1020/102=10
h=10 cm
2 1/3 x (-3 2/7) what does it equal I’m doing “multiplying signed fractions”
Answers
A rectangle has an area of 64 ft squared. If the length of the rectangle is x ft and the width of the rectangle is x to the 1/2 ft, find the length and width of the rectangle.
Answers
Answer:
I DONT KNOW BUT YOU HAVE TO CHECK OUT MY QUESTION NO OE CAN SOLVE IT I BET
Step-by-step explanation:
9(5x) need help asap
Answers
Answer:
45x happy to help ya :)
Step-by-step explanation:
Is (-4,-4) a solution of y> -6x - 1?
Choose 1 answer:
Yes
No
Answers
Answer:
no........... is not the answer
Consider C = {vowels in the word "clinic"}. Find n (C)
A. 6
B. 4
C. 2
D. 12
Answers
Answer:
D galiba ama emin değilim
Answer:
C. 2
Step-by-step explanation:
As you know
Vowels are a , e , i , o , u
"Cl 'i' n 'i' c" so that's 2
1.45 to 4.35 as a simplified fraction
Answers
Answer:
1/45 = 0.02
4/35 =0.1 142857
Step-by-step explanation:
The expression of 1.45 to 4.35 as a fraction in its simplified form is 1/3.
What is a simplified fraction?A simplified fraction is an improper fraction that can no longer be further divided by a divisor. An improper fraction is a fraction with both the numerator and the denominator.
From the information given, we are to express 1.45 to 4.35 as a simplified fraction.
i.e.
= 1.45 as a ratio of 4.35
= 1.45/ 4.35
= 1/3
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Your uncle is 2 years older than 3 times your age! You are 12 years old so how old is your uncle?
Answers
Answer:
18
cuz 2×3=6 so 6 ×3 equals 18
Answer:
38 hrs old
Step-by-step explanation:
3 *12 = 36 + 2 years = 38 years old
find the measure of the missing angle
Answers
Answer:
50
Step-by-step explanation:
40 plus 90 equals 130 and triangle must be 180 so we need 50 degree
50°
Let x be the missing angle.
90°(right angle) + 40°(given) + x = 180° ( the sum of degrees of interior angles of triangle)
x = 180°-130°
x = 50°
What is the square root of -24
Answers
Please help, this is due soon
Answers
Answer:
4
Step-by-step explanation:
If I remember correctly you can not have the arrows on the same y axis