Question

5. For a biology experiment, there are 50 cells present. After 2 hours, there are 1600 bacteria.
How many bacteria would there be in 6 hours? Answer is 163400

Answer 1

To find the answer, we can use exponential growth formula:
N(t) = N₀ * (1+r)^t

Where:
N(t) = Final number of bacteria
N₀ = Initial number of bacteria
r = Growth rate
t = Time in hours

We are given that there are 50 cells initially (N₀ = 50) and after 2 hours, there are 1600 bacteria.

Using these values, we can calculate the growth rate, r:
1600 = 50 * (1+r)^2
Divide both sides by 50:
32 = (1+r)^2

Taking the square root of both sides:
√32 = 1+r
5.656 ≈ 1+r
r ≈ 5.656 - 1
r ≈ 4.656

Now, let's calculate the number of bacteria after 6 hours:
N(t) = 50 * (1+4.656)^6
N(t) ≈ 50 * (1+4.656)^6
N(t) ≈ 50 * (5.656)^6
N(t) ≈ 50 * 163400
N(t) ≈ 8,170,000

Therefore, after 6 hours, there would be approximately 8,170,000 bacteria.