Question

34. A virus decays on a steelsurface at a rate of -15% perhour. There are 5,000,000viruses present on a steelcountertop. Write an equationmodeling the situation andpredict the amount of viruspresent in 24 hours.

Answer 1

In this problem

we have an exponential decay function of the form

`y=a(1-r)^t`

where

a is the initial value --------> a=5,000,000 virus

t is the time in hours

r is the rate -------> r=15%=0.15

y is the amount of virus

substitute given values

`\begin{gathered} y=5,000,000(1-0.15)^t \\ y=5,000,000(0.85)^t \end{gathered}`

For t=24 hours

substitute

`\begin{gathered} y=5,000,000(0.85)^(24) \\ y=101,164\text{ virus} \end{gathered}`