# Polynomial functions, inverses, half-life, investments

Please find the attached.

1) Fit a polynomial Function f(x) to the graph. The scale on the x-axis is 1 and the scale on the y-axis is 5. The point (1,12) is on the graph, Assume that if the graph appears to cross the x-axis at a mark, it really does.

(1,12)

3

2

1 4

2) Noise level in decibels as it depends on the sound intensity (I, in watts/cm2) is defined by the following formula, when Io is the faintest sound the human ear can hear.

DB=10 log (I/Io). where Io= 1x10-16watts/cm2

A) What is the noise level for a sound with intensity 2.5 x 10-9watts/cm2

B) A typical noise level at a rock concert is about 110dB. What is the sound intensity for this noise level?

C) How many times more intense is a 110dB noise than a 45 dB noise?

3) Find the inverse of f(t) = 3t-7/5. if it exists. Check using function composition.

4) Find the time it will take a sample of Plutonium-239 to decay to 0.50% of its original amount if Plutonium-239 has half-life of 24,100 years.

5) How long would it take to triple an investment of $30,000 if it is compounded quarterly at 5.25% annual interest rate?

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#### Solution Preview

Please see the attachment.

1) Fit a polynomial Function f(x) to the graph. The scale on the x-axis is 1 and the scale on the y-axis is 5. The point (1,12) is on the graph, Assume that if the graph appears to cross the x-axis at a mark, it really does.

(1,12)

3

2

1 4

Answer: the Polynomial is y = 3.625x3 - 21.375x2 + 26.75x + 3

2) Noise level in decibels as it depends on the sound intensity (I, in watts/cm2) is defined by the following formula, when Io is the faintest sound the human ear can hear.

DB=10 log ...

#### Solution Summary

This solution is comprised of a detailed explanation to solve olynomial functions, inverses, half-life, and investments questions.