Question

Question 1
5
LA
Expenditure Rate
De Win Enterprises has found that its rate of change of expenditures (in hundreds of dollars per day) on a certain type of job is
give by
f(x) = 4.1x + 1.9
where x is the number of days since the start of the job.
Find the total expenditure if the job takes 12 days.

Answer 1

SOLUTION

The given rate of change function is

$f(x)=4.1x+1.9$

Integrate the function to get the actual function

$\int (4.1x+1.9)dx_{}$

The integral gives

$\begin{gathered} \int (4.1x+1.9)dx_{} \\ =\frac{4.1x^2}{2}+1.9x+C \\ =2.05x^2+1.9x+C \end{gathered}$

The actual function is

$g(x)=2.05x^2+1.9x$

To calculate the expendicure in 12 days

Simply substitute x=12 into the equation

This gives

$g(12)=2.05(12^2)+1.9(12)$

Calcuate the value

$\begin{gathered} g(12)=2.05(144)+22.8 \\ g(12)=295.2+22.8 \\ g(12)=318 \end{gathered}$

Since the expenditure is in hundreds of dollars it follows

$\begin{gathered} g(12)=318\times100 \\ g(x)=318000_{} \end{gathered}$

Therefore the expenditure in 12 days is $318,000