Question

bacteria colonies can increase by 45% every 7 days. if you start with 200 bacteria microorganisms, how large would the colony be after 35 days? first,enter i, the initial (starting) amount. future amount = ?(1 + )^ remember: future amount = i(1 + r)^t

Explanation:

Step1: Identify the initial amount

The initial amount $I = 200$.

Step2: Identify the growth rate

The growth rate $r=0.45$ (since 45% = 0.45).

Step3: Calculate the number of time - periods

The time - period is 7 days. In 35 days, the number of time - periods $t=\frac{35}{7}=5$.

Step4: Calculate the future amount

Using the formula Future Amount $=I(1 + r)^t$, we substitute $I = 200$, $r = 0.45$, and $t = 5$ into the formula.
Future Amount $=200\times(1 + 0.45)^5=200\times1.45^5$.
$1.45^5=1.45\times1.45\times1.45\times1.45\times1.45\approx6.4339$.
Future Amount $=200\times6.4339 = 1286.78\approx1287$.

Answer:

1287