Question

In a laboratory experiment suppose that the population p of an organism is increasing exponentially p(t) = aekt where a and k are constants and t is the number of days after the start of the experiment. If at the beginning of the experiment the number of organism was 100 and after 2 days there were 200 organism. How many of them will be there after 10 days?​

Answer 1

Answer: There will be approximately 2202646.66 organisms after 10 days.

Explanation:

Since at the beginning of the experiment there were 100 organisms and after 2 days there were 200 organisms, we know that the population of the organism increased by a factor of 2 over this time period. This means that k, the exponential growth rate, can be calculated as follows:

k = log(200 / 100) / log(2)

= log(2) / log(2)

= 1

We can now use the formula p(t) = aekt to calculate the number of organisms after 10 days. Since k is equal to 1, we can simplify the formula to p(t) = ae^t:

p(10) = ae^10

We know that at the beginning of the experiment, the number of organisms was 100, so we can set p(0) = 100 and solve for a:

p(0) = 100 = ae^0

a = 100

We can now use this value of a to calculate the number of organisms after 10 days:

p(10) = 100e^10

= 100 * 22026.465795

= 2202646.65795