# A population of bacteria triples every 1.5 hours. If initially there were 200 bacteria, how many...

## Question:

A population of bacteria triples every 1.5 hours. If initially there were 200 bacteria, how many would there be in 125 min?

## Exponential Growth:

Exponential growth occurs when an output value increases by a certain percentage every time the input value increases one whole number. For example, if the {eq}y {/eq}-value doubles every time the {eq}x {/eq}-value increases by {eq}1 {/eq}, the preceding output value is being multiplied by {eq}2 {/eq} to calculate the following output value. The resulting coordinate point set could look like {eq}\{(0, 3), (1, 6), (2, 12), (3, 24), (4, 48), (5, 96), ...\} {/eq} if the starting value was {eq}3 {/eq}.

Exponential growth follows the formula {eq}y=ab^x {/eq}, where {eq}a {/eq} is the initial value and {eq}b {/eq} is the growth factor. In the example above, the equation that represents this scenario is {eq}y=2(3)^x {/eq}.

The population is {eq}\sim {/eq}575.18 bacteria.

Use the exponential growth formula, where the initial value is {eq}200 {/eq}, the growth factor is {eq}3 {/eq}, and the input value, {eq}x {/eq}, is the number of triple lives that have occurred. Since the population triples every hour and a half, which is {eq}130 {/eq} minutes, and only {eq}125 {/eq} minutes have passed. The number of triple lives that have occurred is {eq}\frac{125}{130} {/eq}.

{eq}y=200(3)^{\frac{125}{130}} {/eq}

{eq}y\approx 575.18 {/eq} 