Question

The population of a city can be modeled by P(t) 3810(1.0005)7t , where P(t) is the population after t years. Which function is approximately equivalent to P(t)?

Answer 1

`P(t) = 3810(1.0035)^(t)`

Explanation:

Given:

`P(t) = 3810(1.0005)^(7t)` -----(1)

Simplifying
`(1.0005)^(7t)`

From Law of indices,
`x^(mn) = (x^(m))^(n)`

`(1.0005)^(7t)` =
`(1.0005^(7))^(t)`

When 1.0005 is raised to the 7th power, it is approximately 1.0035.

Substituting
`(1.0005)^(7t) = (1.0035)^(t)` into equation(1)

`P(t) = 3810(1.0035)^(t)`