Question

Because of the rainy season, the depth in a pond increases 3% each week. Before the rainy season started, the pond was 10 feet deep. What is the function that best represents the depth of the pond each week and how deep is the pond after 8 weeks? Round your answer to the nearest foot.
Hint: Use the formula, f(x) = P(1 + r)x.

A. f(x) = 10(0.03)x, 36 feet

B. f(x) = 10(1.03)x, 14 feet

C. f(x) = 10(1.3)x, 37 feet

D. f(x) = 10(1.03)x, 13 feet

Answer 1

After first week pond will be:
10 + 10* 0.03 = 10*(1.03) feet deep
after second week it will be:

10*(1.03) + 10*(1.03)*0.03 = 10*(1.03)^2

from this we can conclude that after x week its will be:
10*(1.03)^x

Note that when second week starts our starting pond is already greater by 3%. every week we add 3% of prevous weeks size of pond

for x = 8 we get
f(x) = 10*(1.03)^8 = 12.66 or rounded 13 feet

Answer is D.