Question

How can I solve this problem? Can someone help me out with understanding this?

The population of viruses in an influenza culture after t hours is given by the function x(t) = `5e^t` (after the "t" is /9.1. I wasn't sure how to put that in.)

The cost y in dollars for a new automated microscope to count x viruses in a sample is y(x) = ln 7x

Create the composite function that calculates the cost y in dollars of counting the number of viruses in an influential culture after t hours.

Answer 1

See explanation below

Explanation:

We have two functions given as:

`f(t)= 5e^t` that gives the number of viruses in t hours

and `g(x)= ln7x` that gives cost for each x viruses

Thus the function that gives cost counting x viruses at t hours is

`(g@f)(t)=g(f(t))=g(5e^t)=ln 7·5e^t= ln 35e^t`

Appliying logarithms rules we have

`(g@f)(t)=g(f(t))=ln35+lne^t=ln 35+t`