Answer:
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.
