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Sagot :
The statement which best compare the mold growth rates is: C. the mold growth rate of the banana bread was half the mold growth rate of the whole wheat bread.
How to compare the mold growth rates?
First of all, we would determine area of mold growth B(t) on the piece of banana bread by using this equation:
B(t) = 20(1.06)^t
At t = 1, we have:
B(t) = 20(1.06)^1
B(t) = 21.2 mm².
At t = 2, we have:
B(t) = 20(1.06)^2
B(t) = 22.47 mm².
At t = 3, we have:
B(t) = 20(1.06)^3
B(t) = 23.82 mm².
At t = 4, we have:
B(t) = 20(1.06)^4
B(t) = 25.25 mm².
Now, we can compare the mold growth rates by using this expression:
B(t) = xW(t)
x = B(t)/W(t)
x = 21.2/40.8
x = 0.5.
At t = 2, we have:
x = 22.47/41.62
x = 0.5.
At t = 3, we have:
x = 23.82/42.45
x = 0.5.
At t = 4, we have:
x = 43.30/25.5
x = 0.5.
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Answer:
(a) The mold growth rate of the banana bread was three times the mold growth rate of the whole wheat bread
Step-by-step explanation:
The equation for exponential growth can be written in the form ...
f(t) = a·b^t
where a is the initial value, and b is the growth factor for time period t. The growth factor is related to the growth rate by ...
b = 1 +r . . . . . where r is the growth rate in time period t
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banana bread
The equation for the area of mold on the banana bread is given as ...
B(t) = 20·1.06^t
Comparing to our generic equation, we see ...
- a = 20
- b = 1.06 = 1 + 0.06
The growth rate of the mold on the banana bread is given as 0.06 = 6% per week.
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whole wheat bread
We are given some values of t and area that we can use to find the growth rate of mold on the whole wheat bread.
W(1) = 40.8 = a·b^1
W(4) = 43.30 = a·b^4
The ratio is ...
W(4)/W(1) = (a·b^4)/(a·b^1) = b^3 = 43.30/40.8
Then the value of b can be found to be ...
b = ∛(43.30/40.8) ≈ 1.02002 ≈ 1 + 0.02
The growth rate of mold on the whole wheat bread is about 0.02 = 2% per week.
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comparison of growth rates
The mold growth rate on the banana bread compared to that on the whole wheat bread is ...
(banana bread growth rate)/(whole wheat bread growth rate) = 6%/2% = 3
We can conclude ...
The mold growth rate of the banana bread was three times the mold growth rate of the whole wheat bread
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