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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

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  1. anonymous
    • one year ago
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    P is the initial value. What is the initial depth?

  2. anonymous
    • one year ago
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    Not sure.

  3. anonymous
    • one year ago
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    It's given in the second sentence of the problem.

  4. anonymous
    • one year ago
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    10?

  5. anonymous
    • one year ago
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    Right. Now r is the percent change from week to week, EXPRESSED AS A DECIMAL. What is r?

  6. anonymous
    • one year ago
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    0.03

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

  8. anonymous
    • one year ago
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    f(x) = P(1 + 0.03) \[^{x}\]

  9. anonymous
    • one year ago
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    1 + 0.03 = 1.03

  10. anonymous
    • one year ago
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    Good. But you can simplify (1+0.03), right?

  11. anonymous
    • one year ago
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    Good. Put it all together.

  12. anonymous
    • one year ago
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    f(x) = 10(1.03)x

  13. anonymous
    • one year ago
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    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
    • one year ago
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    Uhhh do I replace x with 8?

  15. anonymous
    • one year ago
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    In other words, calculate\[f \left( 8 \right) = 10\left( 1.03 \right)^{8} = ?\]

  16. anonymous
    • one year ago
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    14

  17. anonymous
    • one year ago
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    Not what I get. Try again. Remember, calculate 1.03^8 first, then multiply by 10.

  18. anonymous
    • one year ago
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    12.66770081387616 D:

  19. anonymous
    • one year ago
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    Perfect. Round it to get your answer. Well done!

  20. anonymous
    • one year ago
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    Thank You!

  21. anonymous
    • one year ago
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    You're welcome.

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