Question

The population of the random town is 750,000 and 23% of the population becomes a zombie everyday, what function represents p, the number of unaffected people after x days?

Answer 1

Given:

The initial population = 750,000

23% of the population becomes a zombie everyday.

To find:

The function that represents p, the number of unaffected people after x days.

Solution:

The general exponential decay function is:

`P=P_0(1-r)^x` ...(i)

Where,
`P_0` is the initial population, r is the rate of decay and x is the time period.

We know that,

The initial number of unaffected people = 750,000

The unaffected people decreasing by 23% . The decimal form of 23% is 0.23.

Putting
`P_0=750000, r=0.23` in (i), we get

`P=750,000(1-0.23)^x`

`P=750,000(0.77)^x`

Therefore, the required function is
`P=750,000(0.77)^x`, where p is the number of unaffected people after x days.