Question

Brea is growing a culture of bacteria in her lab. At first, the bacteria only covers 2 square inches of space. She feeds it so that it will grow by 50% each day. After one week of growth, the bacteria covers about 34 square inches of space. She uses the equation below to model the growth of bacteria in her lab. A = P(1+r)^t

A) Provide the value of r
B) Calculate the initial amount, P
C) Calculate the time, t
D) Calculate the final amount, A

Answer 1

The growth rate (r) is 0.50, the initial amount (P) is 2 square inches, the time (t) is 7 days, and the final amount (A) is approximately 34 square inches.

Step-by-step explanation:

The student is dealing with a real-world application of exponential growth, modeled by the equation A = P(1+r)^t. Using the provided information:

• A is the final amount of bacteria covering the space after a certain time t.
• P is the initial amount of bacteria.
• r is the growth rate as a decimal.
• t is the time in days.

The growth rate (r) of the bacteria is 50%, which in decimal form is 0.50.

The initial amount (P) of bacteria covering the space is given as 2 square inches.

The time (t) is one week, which is 7 days.

The final amount (A) of bacteria covering the space after one week is approximately 34 square inches.