Let P ( t ) = 10000 ( 1.05 )^ t be the population of a town t years after the year 2000.

Question

Let P(t)=10000(1.05)^t  be the population of a town tt years after the year 2000.

Estimate in which year the population will reach 13401.

Year = 

Answer 1

The question is asking to solve for the variable 't'

You are given 13401 to be the estimated population after "t" years.

The first step is to set the estimated population 13401 equal to the given equation:

P(t) = 10,000(1.05)^t

13401 = 10,000(1.05)^t

Now we can isolate the term with the variable by dividing both sides by 10,000

(13401/10000) = (1.05)^t

We can rewrite this problem as

1.3401 = (1.05)^t

To remove the 't' from the exponent, we can use log properties, to bring down the 't'

log(1.3401) = t log(1.05)

Now we can divide both sides of the equation by log(1.05) to solve for t

log(1.3401)/log(1.05) = t

t = 6 years

By substitution we can confirm the answer

10000(1.05)⁶ = 13401