Question

The population of algae in an
experiment has been increasing by 30%
each day. If there were 100 algae at the
beginning of the experiment, predict the
number of algae in 5 days.
First, complete the equation:
Future Amount = 100(1 +0.30)5
Solve. Round to the nearest whole number.
Future Amount = [ ? ) algae
Enter

Answer 1

Given:

Initial population = 100 algae

Growth rate = 30% per day.

Time = 5 days

To find:

The future amount of population.

Solution:

The exponential growth model is

$y=a(1+r)^t$

where, a is the initial value, r is the rate of interest in percent and t is time period.

Substituting the given values, we get

$y=100(1+\dfrac{30}{100})^5$

$y=100(1+0.30)^5$

Now, solve this.

$y=100(1.30)^5$

$y=100(3.71293)$

$y=371.293$

Therefore, the future value is 371.293 algae.