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Oduvanchick [21]
3 years ago
9

Because of the rainy season, the depth in a pond increases 3% each week. Before the rainy season started, the pond was 10 feet d

eep. 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
Mathematics
1 answer:
kari74 [83]3 years ago
5 0
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.

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