Question

In a lab experiment, a population of 400 bacteria is able to triple every hour. Which equation matches the number of bacteria in the population after 3 hours?
Answer
Multiple Choice Answers
B, equals, 400, left parenthesis, 3, right parenthesisB=400(3)
B, equals, 3, left parenthesis, 1, plus, 400, right parenthesis, cubedB=3(1+400)
3

B, equals, 3, left parenthesis, 400, right parenthesis, left parenthesis, 400, right parenthesis, left parenthesis, 400, right parenthesisB=3(400)(400)(400)
B, equals, 400, left parenthesis, 3, right parenthesis, cubedB=400(3)
3

Answer 1

To determine the number of bacteria in the population after 3 hours, we can use the exponential growth formula:

\[ B(t) = B_0 \cdot r^t \]

Where:
- \( B(t) \) is the population at time \( t \),
- \( B_0 \) is the initial population,
- \( r \) is the growth factor,
- \( t \) is the time in hours.

In this case:
- The initial population \( B_0 = 400 \),
- The bacteria triple every hour, so the growth factor \( r = 3 \),
- The time \( t = 3 \).

Plugging these values into the formula gives us:

\[ B(3) = 400 \cdot 3^3 \]

Calculating \( 3^3 \):

\[ 3^3 = 27 \]

Thus:

\[ B(3) = 400 \cdot 27 = 10800 \]

Now, looking at the multiple-choice options, we can match this to the following option:

**B = 400(3^3)**

This matches the form of the equation we derived. Therefore, the correct choice is:

**B, equals, 400, left parenthesis, 3, right parenthesis, cubed B=400(3^3)**