# A culture started with 2,000 bacteria. After 2 hours, it grew to 2,400 bacteria. Predict how many bacteria will be present after 10 hours?

Aug 29, 2016

4977 bacteria.

#### Explanation:

Growth with bacteria is exponential, so we can consider that we are working with a G.P.

$a = 2000$

$r = \frac{2400}{2000} = 1.2$

If we regard 2 hours as being one time unit, 10 hours is a further 4 units of time. (6th term)

Either 4 more starting with 2400 bacteria,
or 5 time units starting with 2000 bacteria.

After 10 hours: 2000 xx 1.2^5 = 4977 bacteria.

${T}_{6} = 2000 \times {1.2}^{5}$

Or

${T}_{5} = 2400 \times {1.2}^{4}$