# At a certain time, bacteria in a culture has 115,200 bacteria. Four hours later, the culture has 1,440,000 bacteria. How many bacteria will there be in the culture in 15 hours?

##### 2 Answers

I got:

#### Explanation:

I would call the number of bacteria

with

With your numerical data we have:

**At #t=t_1#**

**At #t=t_2=t_1+4#** (4 hours later):

that can be written as:

we can substitute the first equation:

solve it for

using natural logs on both sides we get:

**At #t=t_3=t_1+15#** (15 hours later)

that can be written as:

again we substitute the first equation and the value of

**bacteria will be in** **hours.**

#### Explanation:

Formula for exponential growth is

Where y(t) = Number at time "t" , a = Number at start.

k = rate of growth (when >0) or decay (when <0) ,t = time

After