Question

im1 mini quiz 07: exponential fun...

1. jimmy has just started a new job, where his starting salary is $44000 per year and is expected to increase by 4.6% each year. tina has also just started a new job, which has a starting salary of $43000 per year and is expected to increase at a rate of 6.8% each year.

4a write an equation for $m$, jimmys salary in $t$ years time.
$m = 44000(1.046)^t$
5 nice work!
4b write an equation for $p$, tinas salary in $t$ years time.
$p = 43000(1.068)^t$
5 you got it!
4c how much greater will tinas salary be in 10 years time than jimmys? give your answer correct to the nearest cent.
= ______ dollars
enter your next step here

Explanation:

Step1: Calculate Jimmy's salary at t=10

$M = 44000(1.046)^{10}$
First compute $(1.046)^{10} \approx 1.552969$
Then $M \approx 44000 \times 1.552969 = 68330.636$

Step2: Calculate Tina's salary at t=10

$P = 43000(1.068)^{10}$
First compute $(1.068)^{10} \approx 1.930698$
Then $P \approx 43000 \times 1.930698 = 83019.014$

Step3: Find the salary difference

Subtract Jimmy's salary from Tina's:
$83019.014 - 68330.636 = 14688.378$

Step4: Round to nearest cent

Round $14688.378$ to two decimal places: $14688.38$

Answer:

14688.38 dollars