Question

The population of viruses in an influenza culture after t hours is given by the function
x(t) = 4et/2.5

The cost y in dollars for a new automated microscope to count x viruses in a sample is
y(x) = ln 2x

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

y(t) = y(x(t)) = ln(2*4e^(t/2.5))
= ln(8) + ln(e^(t/2.5))
= ln8 + t/2.5
≈ 0.4t + 2.08