Question

Andre observes that the population of a species grows exponentially over time. Initially, there are 120 organisms of the species. After 6 days, the population grows to 180 organisms.

How many days until the population of the species is 500 organisms? Round your answer to the nearest whole number. (I don't know exactly how to do the work to solve it, I get different answers. But I think the answer is 38?)

Answer 1

The population of the species will reach 500 after 21 days.

Explanation:

The population growth model is expressed as:

P(t) = P₀ e^(r t)

where

• P(t) is the population of the organisms
• P₀ is the initial population of the organisms
• r is the growth rate
• t is the time

Step 1:

We must first calculate the growth rate:

P(6) = 180 = 120 e^(6r)

1.5 = e^(6r)

r = ln(1.5) / 6

r = 0.0676

Step 2:

We can now calculate the time:

P(t) = 500 = 120 e^(0.0676t)

25/6 = e^(0.0676t)

0.0676t = ln(25/6)

t = ln(25/6) / 0.0676

t = 21 days

Therefore, the population of the species will reach 500 after 21 days.