Answer:
.
Step-by-step explanation:
Let C represent total daily charges in dollars and t represent time in hours.
We have been given that a plumber charges $50 for a service call plus $80 per hour.
The amount charged for t hours would be 
.
The total amount charged for t hours would be 
.
We are also told that plumber spends no longer than 8 hours a day at any one site, this means that time t have a restriction as:
Therefore, our required cost function would be .
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2 ln 8 + 2 ln y
The first thing we could do is use the distributive property and "take out" the 2.
After we do that, we get
2( ln 8 + ln y)
Here's a cool property of logarithms of any base.
log a + log b = log ab
Note: The bases of the logarithms must be the same for this to work.
Let's apply that property
2 (ln 8 + ln y)
= 2 ln 8y
That could be your answer. If you want to remove the 2, we can use the following property:
a log b = log (a^b)
2 ln (8y)
= ln (8y)^2
= ln (64y^2)
That could be another answer.
Have an awesome day! :)
