Question

Researchers at the Centers for Disease Control and Prevention have been studying the decay pattern of a new virus with a decay rate of 22% per hour. They start with 500 viruses that they want to check on in the next 8 hours. How many viruses will they find in 8 hours? Round your answer to the nearest whole number.

Answer 1

The researchers will find 86 viruses.

Explanation:

Identify the value of each variable in the formula. Be sure to put the percent in decimal form. Be sure the units match—the rate is per hour and the time is in hours.

A =?

A0 = 500

R= -0.22/hour

t= 8 hours

Substitute the values in the formula.

A= A0e^rt

A= 500e^-0.22x8

Compute the amount.

A ≈ 86.02

Round to the nearest whole number.

A ≈ 86

Answer 2

They will find 69 viruses in 8 hours.

Explanation:

The number of viruses after t hours is given by the following equation:

`V(t) = V(0)(1-r)^(t)`

In which V(0) is the initial number of viruses and r is the decay rate, as a decimal.

They start with 500 viruses

This means that
`V(0) = 500`

Decay rate of 22% per hour.

This means that
`r = 0.22`

So

`V(t) = V(0)(1-r)^(t)`

`V(t) = 500(1-0.22)^(t)`

`V(t) = 500(0.78)^(t)`

How many viruses will they find in 8 hours?

This is V(8).

`V(t) = 500(0.78)^(t)`

`V(8) = 500(0.78)^(8)`

`V(8) = 68.51`

Rounding to the nearest whole number

They will find 69 viruses in 8 hours.