Question

A local newspaper said that the city ofLuttrell is expected to grow by 4% each year.The population in 2012 is 130,457 people.Let t represent the number of years after 2012.Which equation could be used to determinethe total expected population, L. of Luttrell intyears?

Answer 1

Answer:

The equation that could be used to determine the total expected population L of Luttrell in t years is;

$L=130,457\cdot1.04^t$

Explanation:

Given that the city population is expected to grow by 4% each year.

Initially, there were 130,457 people in the city.

$\begin{gathered} r=4\text{\% = 0.04} \\ L_0=130,457 \end{gathered}$

The population at time t from the initial time can be calculated as;

$\begin{gathered} L=L_0(1+r)^t \\ \text{substituting the values;} \\ L=130,457(1+0.04)^t \\ L=130,457(1.04)^t \\ L=130,457\cdot1.04^t \end{gathered}$

Therefore, the equation that could be used to determine the total expected population L of Luttrell in t years is;

$L=130,457\cdot1.04^t$