Question

bacteria colonies can increase by 67% every 2 days. if you start with 55 bacteria microorganisms, how large would the colony be after 10 days? future amount = ?(1 + )^

Explanation:

Step1: Determine the growth factor

The bacteria increase by 67% or 0.67 every 2 - day period. The growth - factor formula for a percentage increase is $1 + r$, where $r$ is the rate of increase. So the growth factor $b=1 + 0.67=1.67$.

Step2: Determine the number of 2 - day periods

The time period is 10 days. Since the growth occurs every 2 days, the number of 2 - day periods $n=\frac{10}{2}=5$.

Step3: Identify the initial amount

The initial number of bacteria $a = 55$.

Step4: Use the exponential - growth formula

The exponential - growth formula is $A=a(1 + r)^n$, where $A$ is the future amount, $a$ is the initial amount, $r$ is the rate of growth per period, and $n$ is the number of periods. Substituting $a = 55$, $r=0.67$, and $n = 5$ into the formula, we get $A = 55\times(1 + 0.67)^5$.

Answer:

$55\times(1 + 0.67)^5$