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
1 answer:
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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