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

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_{} \\ =(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*100 \\ g(x)=318000_{} \end{gathered}`

Therefore the expenditure in 12 days is $318,000