anonymous
  • anonymous
*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
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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anonymous
  • anonymous
P is the initial value. What is the initial depth?
anonymous
  • anonymous
Not sure.
anonymous
  • anonymous
It's given in the second sentence of the problem.

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More answers

anonymous
  • anonymous
10?
anonymous
  • anonymous
Right. Now r is the percent change from week to week, EXPRESSED AS A DECIMAL. What is r?
anonymous
  • anonymous
0.03
anonymous
  • anonymous
Exactly. Now put these values into\[f\left( x \right) = P \left( 1+r \right)^{x}\]What do you get?
anonymous
  • anonymous
f(x) = P(1 + 0.03) \[^{x}\]
anonymous
  • anonymous
1 + 0.03 = 1.03
anonymous
  • anonymous
Good. But you can simplify (1+0.03), right?
anonymous
  • anonymous
Good. Put it all together.
anonymous
  • anonymous
f(x) = 10(1.03)x
anonymous
  • anonymous
Excellent. Now you're down to two possible answers. To calculate the depth after 8 weeks, calculate f(8). What do you get?
anonymous
  • anonymous
Uhhh do I replace x with 8?
anonymous
  • anonymous
In other words, calculate\[f \left( 8 \right) = 10\left( 1.03 \right)^{8} = ?\]
anonymous
  • anonymous
14
anonymous
  • anonymous
Not what I get. Try again. Remember, calculate 1.03^8 first, then multiply by 10.
anonymous
  • anonymous
12.66770081387616 D:
anonymous
  • anonymous
Perfect. Round it to get your answer. Well done!
anonymous
  • anonymous
Thank You!
anonymous
  • anonymous
You're welcome.

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