## anonymous one year ago *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

1. anonymous

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

2. anonymous

Not sure.

3. anonymous

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

4. anonymous

10?

5. anonymous

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

6. anonymous

0.03

7. anonymous

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

8. anonymous

f(x) = P(1 + 0.03) $^{x}$

9. anonymous

1 + 0.03 = 1.03

10. anonymous

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

11. anonymous

Good. Put it all together.

12. anonymous

f(x) = 10(1.03)x

13. anonymous

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

14. anonymous

Uhhh do I replace x with 8?

15. anonymous

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

16. anonymous

14

17. anonymous

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

18. anonymous

12.66770081387616 D:

19. anonymous

20. anonymous

Thank You!

21. anonymous

You're welcome.