1. **State the problem:** We are given the function rule $g(h) = 500 \cdot 4^h$ representing the number of bacteria after $h$ hours. We need to find: a. How many bacteria were there initially? b. How are the bacteria growing each hour? 2. **Recall the formula:** The general form of an exponential growth function is: $$g(h) = g_0 \cdot r^h$$ where $g_0$ is the initial amount (at $h=0$) and $r$ is the growth factor per hour. 3. **Answer to (a): Initial number of bacteria** To find the initial number, evaluate $g(h)$ at $h=0$: $$g(0) = 500 \cdot 4^0 = 500 \cdot 1 = 500$$ So, there were 500 bacteria initially. 4. **Answer to (b): Growth each hour** The base of the exponent, 4, is the growth factor. This means the bacteria population quadruples each hour. In other words, every hour the population is multiplied by 4. **Final answers:** - a. Initial bacteria count is 500. - b. The bacteria grow by a factor of 4 each hour (quadruple every hour).