Question

Here is the function for the number of zombies, N, after t years, with the negative exponent expressed using the fraction ½:

N(t) = 300 • 0.5t/8

What is the half-life for the zombie population?

Answer 1

The half-life for the zombie population is of 8 years.

Explanation:

Exponential equation:

An exponential equation has the following format:

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

In which N(0) is the initial value and the part
`(1-r)^t` is related to the decay.

In this question:

`N(t) = 300(0.5)^{(t)/(8)}`

Thus N(0) = 300, that is, initial population of 300.

What is the half-life for the zombie population?

This is t for which N(t) = 0.5*300 = 150. So

`N(t) = 300(0.5)^{(t)/(8)}`

`150 = 300(0.5)^{(t)/(8)}`

`(0.5)^{(t)/(8)} = (150)/(300)`

`(0.5)^{(t)/(8)} = 0.5`

`(0.5)^{(t)/(8)} = (0.5)^1`

Equal exponents, so:

`(t)/(8) = 1`

`t = 8`

The half-life for the zombie population is of 8 years.