Question

(03.04 MC) Two pieces of bread, banana and whole wheat, were left out on a kitchen counter and mold began to grow on them. The area of mold growth B(t), in mm2, on the piece of banana bread present after time t weeks, can be represented by the equation B(t) = 20(1.06)t. The area of mold growth W(t), in mm2, present on the piece of whole wheat bread after t weeks is represented in the table. t (in weeks) 1 2 3 4 W(t) (in mm2) 40.8 41.62 42.45 43.30 Which statement best compares the mold growth rates of the banana bread and the whole wheat bread? Question 16 options: The mold growth rate of the banana bread was three times the mold growth rate of the whole wheat bread. The mold growth rate of the banana bread was twice the mold growth rate of the whole wheat bread. The mold growth rate of the banana bread was half the mold growth rate of the whole wheat bread. The mold growth rate of the banana bread was a third the mold growth rate of the whole wheat bread.

Answer 1

(a) The mold growth rate of the banana bread was three times the mold growth rate of the whole wheat bread

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