Two towns had a population of 12,000 in 1990. By 2000, the population of town A...

Two towns had a population of 12,000 in 1990. By 2000, the population of town A had increased by 13⁢ % while the population of town B had decreased by 13⁢ %. Assume these growth and decay rates continued.

a. Write two exponential population models A(T) and B(T) for towns A and B, respectively, where T is the number of decades since 1990.

A(T)=

12000*e0.12*T

B(T)=

12000*e−0.14*T

b. Write two new exponential models a(t) and b(t) for towns A and B, where t is the number of years since 1990.

Give the answers in the form C⋅at. Round the growth factor to four decimal places.

a(t)=

12000*1.13t

b(t)=

12000*0.87t

c. Find A(2), B(2), a(20), and b(20) and explain what you have found.

Round your answers to the nearest integer.

A(2)=

B(2)=

a(20)=

b(20)=

Each of these values represent the population

2 years after 199020 decades after 19902 decades after 1990

Solutions

Expert Solution

milcah answered 1 year ago

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