Question

You get a raise of 3.5% each year.

Answer 1

Using an exponential function, it is found that:

a) The doubling time of the salary is of approximately 20 years.

b) The salary will be of $160,000.

What is an exponential function?

An increasing exponential function is modeled by:

$A(t) = A(0)(1 + r)^t$

In which:

• A(0) is the initial value.

• r is the growth rate, as a decimal.

The growth rate for this problem is:

r = 0.035.

The doubling time is t for which A(t) = 2A(0), hence:

$A(t) = A(0)(1 + r)^t$

$2A(0) = A(0)(1.035)^t$

$(1.035)^t = 2$

$\log{(1.035)^t} = \log{2}$

$t\log{1.035} = \log{2}$

$t = \frac{\log{2}}{\log{1.035}}$

t = 20 years.

You retire in 40 years, which is 2 doubling periods, hence the salary will be of:

40000 x 2 x 2 = $160,000.

More can be learned about exponential functions at brainly.com/question/25537936

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