Exponential Functions — Question 5

Question 5

A scientist is growing a bacteria culture in a lab. The population of bacteria at time $t$ hours is given by the function: $$P(t) = 1200e^{0.55t}$$

• What is the population after 4 hours?

• After how many hours will the population reach 10,000?

• By what percentage does the population increase each hour?

Round all answers to two decimal places.

Question 5 - Solution

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

(a)

$$P(4)=1200e^{2.2}$$

$$\boxed{10830.02\quad\text{bacteria}}$$

(b)

$$t=\ln(10000/1200)/0.55$$

$$\boxed{3.86\quad\text{hours}}$$

(c)

$$100(P(t+1)/P(t)-1)=100(e^{0.55}-1)$$

$$\boxed{73.33\quad\text{\%}}$$