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A biologist estimates that an area has a population of 2,500 rabbits. If the population increases at a rate of 6.8% per month, then how many months before there are 3,200 rabbits?

Sagot :

sqdancefan

Answer:

  3.75 months

Step-by-step explanation:

You want the number of months it takes to increase from 2500 to 3200 at the rate of 6.8% per month.

Exponential function

The exponential function describing the population can be written as ...

  population = (initial number) × (growth factor)^n

where "growth factor" is the multiplier of the population for each time period. The growth factor is (1 + growth rate) = (1 + 6.8%) = 1.068.

We want to find n, the number of time periods required to make the population become 3200, if the initial number is 2500:

  3200 = 2500 × 1.068^n

  3200/2500 = 1.068^n . . . . . . . . . divide by 2500

  log(32/25) = n·log(1.068) . . . . . . . take logarithms

  n = log(32/25)/log(1.068) ≈ 3.7524

It will be about 3.75 months before there are 3200 rabbits.

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