Exponential Functions — Question 1

Question 1

The population of a bacterial culture is modeled by the function $$P(t) = 500e^{0.3t}$$ where $t$ is measured in hours.

• What is the population after 5 hours?

• After how many hours will the population reach 3000?

• By what factor does the population grow every 4 hours?

Round your answers to two decimal places.

Question 1 - Solution

Use the exact exponential model and keep full precision until the final rounding.

(a)

$$P(5)=500e^{1.5}$$

$$\boxed{2240.84\quad\text{bacteria}}$$

(b)

$$500e^{0.3t}=3000\ \Longrightarrow\ t=\ln(6)/0.3$$

$$\boxed{5.97\quad\text{hours}}$$

(c)

$$P(t+4)/P(t)=e^{1.2}$$

$$\boxed{3.32\quad\text{growth factor}}$$