Question

A sample of bacteria is decaying according to a half-life model. If the sample begins with 200 bacteria and after 5 minutes there are 150 bacteria, how many bacteria will remain after 7 minutes? Round your answer to the nearest whole number, and do not include units.

Answer 1

Hello!

The answer is:

There will remain a total of 134 bacteria after 7 minutes.

Why?

Exponential decay calculations are commonly used to find the decrease of amounts of populations, bacterias, and other situations when using proportional relationships. In order to find the problem, we must remember the equation used to calculate the exponential decay.

$Decay=S(1-r)^{t}$

Where,

S, is the starting value/amount

r, is the rate (% to real number)

t, is the time elapsed.

We are given that the numbers of bacteria decrease by 50 after 5 minutes, starting with 200, and after 5 minutes the number of bacteria is 150

Calculating the rate of decrease, we have:

$Rate=\frac{Decrease}{Starting}=\frac{200-150}{200}=\frac{50}{200}=0.25$

Therefore, the rate of decrease is 0.25 or 25% (after multiplying the number by 100)

Then, substituting the given information and the rate of decrease into the decay equation, we have:

$Decay=200(1-0.25)^{\frac{t}{5}}$

Now, to calculate how many bacteria will remain after 7 minutes, we need to substitute it into the decay equation:

$Bacteria(After7Minutes)=200(1-0.25)^{\frac{7}{5}}=133.69$

So, rounding to the nearest whole number, there will remain a total of 134 bacteria after 7 minutes.

Have a nice day!