Question

1. interpret the exponential function as growth of an initial quantity over time - week 13 - (section 4.1)

• write a function that describes the growth over time (t) of a population p, whose initial amount p₀ triples every year. solution:

Explanation:

Step1: Recall Exponential Growth Formula

The general formula for exponential growth is \( P(t) = P_0 \cdot a^t \), where \( P_0 \) is the initial quantity, \( a \) is the growth factor, and \( t \) is time.

Step2: Determine the Growth Factor

The population triples every year, so the growth factor \( a = 3 \).

Step3: Substitute into the Formula

Substitute \( a = 3 \) into the exponential growth formula. So the function is \( P(t) = P_0 \cdot 3^t \), where \( t \) is in years.

Answer:

The function describing the population growth is \( P(t) = P_0 \cdot 3^t \) (where \( t \) represents time in years, \( P_0 \) is the initial population, and \( P(t) \) is the population at time \( t \)).