Question

The formula a=119e^0.027t models the population of a particular city, in thousands, t years after 1998, when will the population of the city reach 178 thousand

Answer 1

By year 2092

Explanation:

In this question, we are asked to calculate the year at which the population of the city will reach 178,000

The equation that models the population of the city is given as;

A = 119e^0.027t

Here, we plug A to be 178,000

178000 = 119e^0.027t

we take the natural logarithm of both sides)

ln 178,000 = ln (119e^0.027t)

12.09 = 0.027t ln 119

12.09/ln 119 = 0.027t

2.53 = 0.027t

t = 2.53/0.027

t = 93.7 which is approximately 94 years

Since t is number of years after 1998, the exact time the population will reach 178,000 will be 1998 + 94 years = 2,092

Answer 2

The population of the city will reach 178 thousand almost 15 years after 1998, that is, in the last months of 2012.

Explanation:

The equation to be solved is:

`178 = 119\cdot e^(0.027\cdot t)`

Now, the variable is cleared with the help of algebraic handling:

`(178)/(119) = e^(0.027\cdot t)`

`\ln (178)/(119) = 0.027\cdot t`

`t = 37.037\cdot \ln (178)/(119)`

`t \approx 14.913\,yr`

The population of the city will reach 178 thousand almost 15 years after 1998, that is, in the last months of 2012.