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guajiro [1.7K]
3 years ago
11

A biologist is studying the elk population in a county park. She starts with only 2 elk and observes that the number of elk trip

les every year. Which equation can be used to find the number of years, y, it will take for the population to reach 1,458 elk?
Mathematics
1 answer:
DochEvi [55]3 years ago
8 0

Answer:

The expression that represents the population of elk is: \text{elk}(t) = 2*3^t. It'll take 6 years for the population to reach 1,458 individuals.

Step-by-step explanation:

Since the number of elks triples every year and starts at \text{elk}(0) = 2, then after the first year the population will be:

\text{elk}(1) = \text{elk}(0)*3 = 2*3

While on the second year, it'll be:

\text{elk}(2) = \text{elk}(1)*3 = 2*3*3 = 2*3^2

On the third year:

\text{elk}(3) = \text{elk}(2)*3 = 2*3^2*3 = 2*3^3

And so on, therefore the expression that describes the population of elk as the years passes is:

\text{elk}(t) = 2*3^t

If we want to know the number of years until the population reach 1,458 elk, we need to apply this value to the left side of the equation and solve for t.

1458 = 2*3^t\\3^t = \frac{1458}{2}\\3^t = 729\\ln(3^t) = ln(729)\\t*ln(3) = ln(729)\\t = \frac{ln(729)}{ln(3)} = 6

The population will reach 1,458 elk in 6 years.

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<u />

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