Question

David placed a cupcake in his locker a few days ago. At the time he put it in, the cupcake had 300 bacteria on it. The number of bacteria is growing by 25% each day. 11. Write an equation to represent the context. 12. How much bacteria will be on the cupcake after 2 weeks?

Answer 1

The growth equation is

$y=a(1+r)^x$

Where:

a is the initial amount

r is the rate of growth in decimal

Since at the time he put the cupcake, there were 300 bacteria

Then a = 300

Since the bacteria is growing by 25%

r = 25/100 = 0.25

Substitute them in the form of the equation above

$y=300(1+0.25)^x$

Since in 2 weeks, there are 2 x 7 = 14 days

Then x = 14

Substitute x by 14 to find y

$\begin{gathered} y=300(1.25)^{14} \\ y=6821.21 \end{gathered}$

Round it to the nearest whole number

The number of bacteria after 2 weeks is 6821