Exponential Functions Question 1 The population of a city wa

Exponential Functions Question 1: The population of a city was 82,000 in the year 2000 and 86,400 in the year 2010. If the population grows exponentially, determine the population of the city in the year 2020. In the year 2020, the population will be: Less than 91,000 Between 91,000 and 91,200 Between 91,200 and 91,400 Between 91,400 and 91,600 More than 91,600 Save

Solution

general exponential growth equation is P(t)=(P(0))b^t

P(0) is initial popultaion, t is time in years, a and b are constant, P(t) is population after time t.

let t=0 corresponds to year 2000

=>t=10 corresponds to year 2010 ,t=20 corresponds to year 2020

P(0)=82000, P(10)=86400

=>86400=82000b¹⁰

=>b¹⁰=(86400_/82000)

=>b=(216_/205)^1_/10

P(t)=82000((216_/205)^1_/10)^t

P(t)=82000((216_/205)^t_/10)

population in year 2020 is =P(20)

population in year 2020 is =82000((216_/205)^20_/10)

population in year 2020 is =82000((216_/205)²)

population in year 2020 is =91036

between 91000 and 91200