1. Bonshaw is growing at a rate of 5% per year. If the current population is 340, how long will it take before it hits 500 people?

Question

Answer 1

### Approximately 7.31 years

Answer 2

## Step 1: Calculate the growth factor### The population grows by 5% each year, meaning it multiplies by

each year. This is the growth factor.## Step 2: Set up the growth equation### Let

be the initial population (340),

be the population after

years, and

be the growth factor (1.05). The equation for exponential growth is

. We want to find

when

. So,

.## Step 3: Solve for t### Divide both sides by 340:

. This simplifies to

.### Take the logarithm of both sides:

.### Solve for t:

.

Question