Question

If a culture starts with 500 bacteria and doubles every hour, how many bacteria will there be after 4 hours?

• A. $4 \times 10^3$
• B. $8 \times 10^3$
• C. $6 \times 10^3$
• D. $5 \times 10^3$

Hint:

Exponential growth can be calculated using the formula \( N(t) = N_0 \times 2^t \), where \( N_0 \) is the initial amount, and \( t \) is the time elapsed. Each hour, the population doubles.

Answer 1

The Correct Option is B

In this problem, the number of bacteria doubles every hour, which follows an exponential growth pattern. The formula for exponential growth is: \[ N(t) = N_0 \times 2^t \] Where:
- \( N(t) \) is the number of bacteria at time \( t \).
- \( N_0 \) is the initial number of bacteria.
- \( t \) is the time in hours.
Given:
- Initial bacteria \( N_0 = 500 \).
- Time \( t = 4 \) hours.
Substitute these values into the formula: \[ N(4) = 500 \times 2^4 = 500 \times 16 = 8000 = 8 \times 10^3 \] Thus, the number of bacteria after 4 hours is \( 8 \times 10^3 \). Therefore, the correct answer is option (2).