Question

The population P of a certain city can be modeled by P=19000e0.0215t where T represent the number of years since 2000. When t=1 the year is 2001 when t =2 the year is 2002 based in yhis model in what year will the population reach 40,000

Answer 1

Explanation:

The population P of a certain city can be modeled by

P=19000e0.0215t

where T represent the number of years since 2000.

When t=1 the year is 2001

when t =2 the year is 2002. This means that

When t=0 the year is 2000

To determine the year when the population will be 40,000 , we will substitute P = 40,000 and solve for t. It becomes

40000 = 19000e^0.0215t

40000 / 19000 = e^0.0215t

2.105 = e^0.0215t

Take ln of both sides

0.7443 = 0.0215t

t = 0.7443/0.0215

t = 34.62

Approximately 35 years

So the year will be 2035