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? Explain in terms of exponents. (To type an exponent, use the ^ key.)

Answer 1

The correct answer should be: Eight years. To get ½ of the 300, you need 0.5^(t/8) to equal ½, or 0.5. That means that the exponent must be 1. This happens when t = 8 years.

Answer 2

Half life period of zombies is 8 years.

Explanation:

The function for the numbers of zombies N, after t years with negative exponent expressed using the fraction
`(1)/(2)` is

`N(t) = 300.((1)/(2))^{(t)/(8)}`

Now we have to calculate the half life period for the zombies population.

That means we have to calculate the time in which zombies population gets half of the initial population.

So for
`N(t)=(300)/(2)=150` we have to calculate the time t.

By putting the value of N(t) = 150 in the function.

`150=(300).((1)/(2))^{(t)/(8)}`

`((1)/(2))^{(t)/(8)}=(150)/(300)=((1)/(2))`

Or
`((1)/(2))^{(t)/(8)}=((1)/(2))^(1)`

Here we will equate the powers of same fraction

`(t)/(8)=1`

t = 8 years

Therefore half life period of zombies population is 8 years.