Answer:
Option D)
[tex]S(t) = 24400\times \ln(3.3t)[/tex]
The average rate of change in Elija's salary between is $7452.50 per year.
Step-by-step explanation:
We are given the following in the question:
S(t) represent the Elija's salary.
S(t) can be obtained by multiplying starting annual salary, $24,400, by the natural logarithm of the product of 3.3 and the number of years since 2010, t.
Thus, we can write:
[tex]S(t) = 24400\times \ln(3.3t)[/tex]
Average rate of change of function =
[tex]\displaystyle\frac{\delta S}{\delta t} = \frac{S(b)-S(a)}{b-a}[/tex]
Putting b = 2015-2010 = 5, a = 2012-2010 = 2
We evaluate S(5) and S(2)
[tex]S(t) = 24400\times \ln(3.3t)\\S(5) = 24400\times \ln(3.3\times 5)\\S(2) = \24400\times \ln(3.3\times 2)[/tex]
Average rate of change =
[tex]\displaystyle\frac \frac{S(b)-S(a)}{b-a}\\\\= \frac{S(5)-S(2)}{5-2}\\\\=\frac{24400(\ln(3.3\times 5)-\ln(3.3\times 2))}{3}\\=7452.50[/tex]
The average rate of change in Elija's salary is $7452.50 per year.
