Question

Question 1(Multiple Choice Worth 5 points) (04.03 MC) 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. f(x) = 10(0.03)x, 36 feet f(x) = 10(1.03)x, 14 feet f(x) = 10(1.3)x, 37 feet f(x) = 10(1.03)x, 13 feet

Answer 1

In this problem, you are to create an algrebraic formula to describe the progression of the depth of the pond with respect to time. In fact, you are already given with the general formula: f(x) = P(1 + r)x. All you have to do is find the value of P, r and x, to determine f(x) which stands for the depth.

I think P is the principal amount of depth. This is the base depth before the experiment has even started. Hence, P=10 feet. Then, r is the rate of change. Since it was mentioned that the depth increases by 3% each week, r = 3% or 0.03. Lastly, you want to find the depth after 8 weeks, so x=8. Therefore, the formula becomes:

f(x) = 10(1+0.03)*8 = 82.4

However, this is not one of the choices. There must be some typographical error. The equation must be f(x) = P(1+r)^x. Using this equation instead,

f(x) = 10(1+0.03)^8 = 13 ft