Question

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

Answer 1

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

Answer 2

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.