Suppose you take a job that has starting annual pay of 3800 each yeah you were receive a raise and you have two options to choose from An increase of 1000 each year an increase of 3% each year 1.Which option models exponential growth 2.Which option earns more money after year 1? 3.Which option earn more money after year 7?

Let's wrote both equations:

In both cases, we start at $3800.

For the case where you have an increase of $1000 per year, the yearly pay as a number of years, x, will be:

f(x) = $3800 + x*$1000

In the case where we have an increase of 3%, the first year the annual pay will be:

$3800 + (3%/100%)*$3800 = $3800*(1.03)

The next year, the annual pay will be:

$3800*(1.03) + (3%/100%)*($3800*(1.03)) = $3800*(1.03)^2

You already can see the pattern, after x years, your annual pay will be:

g(x) = $3800*(1.03)^x

1) Which option models exponential growth?

This is g(x) = $3800*(1.03)^x, the case where you get an increase of the 3% each year.

2) Which option earns more money after year 1?

we can evaluate both functions:

f(1) = $3800 + $1000*1 = $4800

g(1) = $3800*(1.03) = $3914

Then the case where you get $1000 per year earns more money after only one year.

3) Which option earn more money after year 7?

Let's evaluate both functions in x = 7.

f(7) = $3800 + $1000*7 = $10800

g(7) = $3800*(1.03)^7 = $4673.5

Still the first option is better.

good luck on your studies! : )

david edward.

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