Question

To model the number of bacteria in a petri dish, a scientist uses the function N(t)=1,000(1.3)t, where t is the number of hours since the start of the experiment. According to the model, how does the number of bacteria change over time?

Answer 1

According to the model N(t)=1,000(1.3)^t, the number of bacteria increases exponentially over time. This is because the term (1.3)^t represents exponential growth, where the number of bacteria grows by a factor of 1.3 every hour. As t increases, the exponentiation of 1.3 to larger values results in a rapid increase in the number of bacteria in the petri dish. The growth is not linear but rather exponential, meaning that the rate of increase is continuously accelerating.