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

Answer:

$P(t) = 3810(1.0035)^{t}$

Step-by-step 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)

$P(t) = 3810(1.0035)^{t}$