Question

In a lab experiment, a population of 200 bacteria is able to quadruple every hour. Which equation matches the number of bacteria in the population after 2 hours?
Answer
Attempt 1 out of 3
Multiple Choice Answers
B, equals, 4, left parenthesis, 1, plus, 200, right parenthesis, squaredB=4(1+200)
2

B, equals, 200, left parenthesis, 1, plus, 4, right parenthesis, squaredB=200(1+4)
2

B, equals, 4, left parenthesis, 200, right parenthesis, left parenthesis, 200, right parenthesisB=4(200)(200)
B, equals, 200, left parenthesis, 4, right parenthesis, left parenthesis, 4, right parenthesisB=200(4)(4)

Answer 1

To solve the problem of how many bacteria there are after 2 hours given that the population quadruples every hour, we start with an initial population of 200 bacteria.

After 1 hour, the population will quadruple:
\[
200 \times 4 = 800 \text{ bacteria}
\]

After 2 hours, the population will again quadruple:
\[
800 \times 4 = 3200 \text{ bacteria}
\]

We can also express this mathematically using the formula for exponential growth. The general formula for a population that quadruples (i.e., grows by a factor of 4) every hour can be written as:
\[
B(t) = B_0 \cdot 4^t
\]
where \(B_0\) is the initial population, and \(t\) is the time in hours. Substituting the values we have:
\[
B(2) = 200 \cdot 4^2
\]
Calculating \(4^2\):
\[
4^2 = 16
\]
Thus:
\[
B(2) = 200 \cdot 16 = 3200
\]

Now, looking at the multiple choice options you provided, the correct equation representing the number of bacteria after 2 hours would be one that corresponds to:
\[
B = 200 \cdot 4^2
\]
This matches the expression \(B = 200(4)(4)\), corresponding to the growth over two hours.

So the correct answer from the options you provided is:
\[
B = 200(4)(4)
\]