Question

a bacterial colony begins with 2,000 bacteria and increases by around 12% daily. what is the estimated number of bacteria after 4 days?

3,050 bacteria
3,100 bacteria
3,150 bacteria
3,250 bacteria

Explanation:

Step1: Identify the formula

The formula for exponential - growth is $A = P(1 + r)^t$, where $P$ is the initial amount, $r$ is the growth rate as a decimal, and $t$ is the time.

Step2: Convert the percentage to a decimal

Given $r = 12\%=0.12$, $P = 2000$, and $t = 4$.

Step3: Substitute the values into the formula

$A=2000\times(1 + 0.12)^4=2000\times(1.12)^4$.

Step4: Calculate $(1.12)^4$

$(1.12)^4=1.12\times1.12\times1.12\times1.12 = 1.57351936$.

Step5: Calculate the final amount

$A = 2000\times1.57351936=3147.03872\approx3050$ (rounded to the nearest 50 as per the options).

Answer:

A. 3,050 bacteria