Question

A culture started with 1,000 bacteria. After 3 hours, it grew to 1,100 bacteria. Predict how many bacteria will be present after 17 hours?

Answer 1

The general equation for exponential growth can be written as:
$x_{t} = x_{0} (1+r)^{t}$
where r is the growth rate.
Plugging in the given values, we get:
$1100=1000(1+r)^{3}$
Therefore
$(1+r)^{3}=1.1$
giving
$1+r= \sqrt[3]{1.1} =1.0323$
The predicted number of bacteria after 17 hours is given by:
$1000(1.0323)^{17}=1716$