Question

*MEDAL and FAN*

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

P is the initial value. What is the initial depth?

Answer 2

Not sure.

Answer 3

It's given in the second sentence of the problem.

Answer 4

10?

Answer 5

Right. Now r is the percent change from week to week, EXPRESSED AS A DECIMAL. What is r?

Answer 6

0.03

Answer 7

Exactly. Now put these values into\[f\left( x \right) = P \left( 1+r \right)^{x}\]What do you get?

Answer 8

f(x) = P(1 + 0.03) \[^{x}\]

Answer 9

1 + 0.03 = 1.03

Answer 10

Good. But you can simplify (1+0.03), right?

Answer 11

Good. Put it all together.

Answer 12

f(x) = 10(1.03)x

Answer 13

Excellent. Now you're down to two possible answers. To calculate the depth after 8 weeks, calculate f(8). What do you get?

Answer 14

Uhhh do I replace x with 8?

Answer 15

In other words, calculate\[f \left( 8 \right) = 10\left( 1.03 \right)^{8} = ?\]

Answer 16

14

Answer 17

Not what I get. Try again. Remember, calculate 1.03^8 first, then multiply by 10.

Answer 18

12.66770081387616 D:

Answer 19

Perfect. Round it to get your answer. Well done!

Answer 20

Thank You!

Answer 21

You're welcome.