Question

A petri dish of bacteria grow continuously at a rate of 200% each day. If the petri dish began

with 10 bacteria, how many bacteria are there after 5 days? Use the exponential growth
function f(t) = ger and give your answer to the nearest whole number. Show your work.

Need the answer ASAP

Answer 1

Answer: 2430 bacteria.

Explanation:

When we have a quantity A, and we have an increase of the X%, the new quantity can be written as:

A + (X%/100%)*A

In this case, we have A = 10 bacteria.

And X% = 200%.

Then if we start with 10 bacteria.

After one day, we will have:

10 bacteria + (200%/100%)*10 bacteria

= 10 bacteria + 2*10 bacteria = 3*10 bacteria.

After another day, we will have:

3*10 bacteria + (200%/100%)*(3*10 bacteria)

3*10 bacteria + 2*(3*10 bacteria)

3*(3*10 bacteria)

10 bacteria*(3)^2

We already can see the pattern here.

After t days, we will have:

10 bacteria*(3)^t.

This is the equation f(t) we wanted:

f(t) =10 bacteria*(3)^t

after 5 days, we will have:

f(5) = 10 bacteria*(3)^5 = 2430 bacteria.