Question

For a certain strain of bacteria, k is 0.255 when t is measured in days. How long will it take for 2 bacteria to become 2000?

a) 16 days
b) 7824 days
c) 1960 days
d) 10 days

Answer 1

It will take approximately 2.54 days for 2 bacteria to become 2000.

Step-by-step explanation:

To solve this problem, we will place the formula for exponential growth:

N = N₀ * 2t / k

Where N is the final number of bacteria, N₀ is the initial number of bacteria, t is the time in days, and k is the growth constant. We are given that N₀ = 2, N = 2000, and k = 0.255 (measured in days). Setting these values into the equation, we get:

2000 = 2 * 2t / 0.255

Divide both the L.H.S and R.H.S of the equation by 2 to separate the exponential term:

1000 = 2t / 0.255

Now, take the logarithm of L.H.S and R.H.S sides to solve for t:

log2(1000) = t / 0.255

Using a calculator to perform the logarithm, we get:

t / 0.255 ≈ 9.966

Multiply both sides of the equation by 0.255 to solve for t:

t ≈ 2.54

So, it will take approximately 2.54 days for 2 bacteria to become 2000.