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?

## Step 1: Calculate the growth factor<br />### The population grows by 5% each year, meaning it multiplies by $1 + 0.05 = 1.05$ each year. This is the growth factor.<br /><br />## Step 2: Set up the growth equation<br />### Let $P_0$ be the initial population (340), $P(t)$ be the population after $t$ years, and $r$ be the growth factor (1.05). The equation for exponential growth is $P(t) = P_0 \cdot r^t$. We want to find $t$ when $P(t) = 500$. So, $500 = 340 \cdot (1.05)^t$.<br /><br />## Step 3: Solve for t<br />### Divide both sides by 340: $\frac{500}{340} = (1.05)^t$. This simplifies to $\frac{25}{17} = (1.05)^t$.<br />### Take the logarithm of both sides: $\ln(\frac{25}{17}) = t \cdot \ln(1.05)$.<br />### Solve for t: $t = \frac{\ln(\frac{25}{17})}{\ln(1.05)} \approx \frac{0.3567}{0.0488} \approx 7.31$.