Question

A zombie infection in Tonky public schools grows by 15% per hour. The initial group of zombies was 4 freshman. How many zombies are there after 14 hours ?

Answer 1

Solution

A zombie infection in Tonky public schools grows by 15% per hour.

The formula for exponential growth is

$y=a(1+r)^t_{}$

Where

$\begin{gathered} a\text{ is the }initial\text{ amount} \\ r\text{ is the }growth\text{ rate} \\ t=time\text{ intervals} \end{gathered}$

The initial group of zombies was 4 freshman, i.e

$a=4$

The growth rate, r is

$\begin{gathered} r=\frac{15}{100}=0.15 \\ r=0.15 \end{gathered}$

The exponential growth equation is

$\begin{gathered} y=a(1+r)^t \\ y=4(1+0.15)^t \\ y=4(1.15)^t \end{gathered}$

After 14 hours, i.e t = 14 hours, the number of zombies there is

$\begin{gathered} y=4(1.15)^t \\ \text{Where t}=14hours \\ y=4(1.15)^{14} \\ y=28.30282 \\ y=28\text{ (nearest whole number)} \end{gathered}$

Hence, the number of zombies after 14 hours is 28 (nearest whole number)