1 This exercise uses the population growth model The populat

1. This exercise uses the population growth model.

The population of a country has a relative growth rate of 4% per year. The government is trying to reduce the growth rate to 3%. The population in 2011 was approximately 120 million. Find the projected population for the year 2032 for the following conditions. (Round your answers to the nearest whole number.)

(a) The relative growth rate remains at 4% per year.
million people

(b) The relative growth rate is reduced to 3% per year.
million people

2. This exercise uses the population growth model.

The bat population in a certain Midwestern county was 270,000 in 2012, and the observed doubling time for the population is 32 years.

(a) Find an exponential model

n(t) = n₀2^t/a

for the population t years after 2012.

n(t) =   

(b) Find an exponential model

n(t) = n₀e^rt

for the population t years after 2012. (Round your r value to four decimal places.)

n(t) =   

Solution

1. We have to use the following formula

N(t)= N(0) e^rt

N(t) is the population after t years

N(0) is the population in 2012

r is the rate of growth that is 4%=.04

t=2032-2011= 21 yrs

N(21)=110 e^{.04 *21}

N(21)= 255 million

b. When r=3%=.03

N(21)=110 e^.03*21

        =207 million