Write an exponential growth function. Explain why your function represents exponential growth. (4 points) in three sentences

Answer 1

An example of an exponential growth function is \( f(t) = 3e^{0.5t} \), where \( e \) is the base of the natural logarithm, approximately equal to 2.71828, and \( t \) represents time. This function represents exponential growth because the value of \( f(t) \) increases at a rate proportional to its current value, meaning as \( t \) increases, the function grows faster and faster, creating a J-shaped curve when graphed. Specifically, the positive coefficient \( 0.5 \) indicates that the growth rate is constant over time, leading to rapid increases as \( t \) becomes large.