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A deer population grows at a rate of four percent per year. How many years will it take for the population to double?

User RichardW
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2 Answers

5 votes

Answer:it will take approximately 18 years

Explanation:

A deer population grows at a rate of four percent per year. The growth rate is exponential. We would apply the formula for exponential growth which is expressed as

A = P(1 + r/n)^ nt

Where

A represents the population after t years.

n represents the period of growth

t represents the number of years.

P represents the initial population.

r represents rate of growth.

From the information given,

A = 2P

P = P

r = 4% = 4/100 = 0.04

n = 1

Therefore

2P = P(1 + r/n)^ nt

2P/P = (1 + 0.04/1)^1 × t

2 = (1.04)^t

Taking log of both sides to base 10

Log 2 = log1.04^t = tlog1.04

0.3010 = t × 0.017

t = 0.3010/0.017 = 17.7 years

User Erman
by
8.1k points
5 votes

Answer:

It is going to take 17.65 years for the population to double.

Explanation:

The population of the deer is after t years is given by the following equation


P(t) = P_(0)(1 + r)^(t)

In which
P_(0) is the initial population and r is the decimal growth rate.

A deer population grows at a rate of four percent per year. This means that
r = 0.04

How many years will it take for the population to double?

This is t when
P(t) = 2P_(0)


P(t) = P_(0)(1.04)^(t)


2P_(0) = P_(0)(1.04)^(t)


(1.04)^(t) = 2

Here, we apply the log 10 to both sides of the equation.

It is important to note the following property of logarithms.


\log{a^(t)} = t\log{a}


\log{(1.04)^(t)} = \log{2}


t\log{1.04} = 0.3


0.017t = 0.3


t = (0.3)/(0.017)


t = 17.65

It is going to take 17.65 years for the population to double.

User Steenhulthin
by
8.8k points

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