Question

Please super important!!! 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.

Answer 1

21 days

Explanation:

180 = 120 b^(6k)

ln(1.5) = 6k ln(b)

k = ln(1.5)/6

500 = 120 e^((ln(1.5)/6)t)

ln(25/6) = (ln(1.5)/6)t ln(e)

t = (ln(25/6)*6)/ln(1.5)

t = 21 days

Answer 2

32 days

Explanation:

First, you must find out how much the organisms grew:

180 - 120 = 60

Then, you must find how many organisms grew in a day:

60 ÷ 6 = 10

So, we know that in one day 10 organisms grow. But how many more days until the species reaches 500?

500 - 180 = 320

So, 320 organisms have to grow to become 500. Now, we need to find how many days it will take for the population to grow to 320.

320 ÷ 10 = 32

So it will take 32 days until the population of the species is 500.

Hope this helps you out ; )