Question

Suppose it takes

12
hours for a certain strain of bacteria to reproduce by dividing in half. If
45
bacteria are present to begin with, the total number present after
x
days is

f
(
x
)
=
45
⋅
4
x
.

Find the total number present after
1
,
2
, and
3
days.

Answer 1

Explanation:

The formula is

`y=45(4)^x`

which models the exponential function

`y=a(b)^x` where a is the initial amount of whatever it is you have (in our case it's bacteria), b is the growth rate (ours is 4 which means that every day the number from the day before increases by a factor of 4), and x is the number of days. We plug into the formula the values we have, starting with x = 1:

`y=45(4)^1`

Always raise what's inside the parenthesis first, then multiply in the 45. 4 to the first is 4, and 4 multiplied by 45 is 180. After the first day, there are 180 bacteria present in the culture.

Next, x = 2:

`y=45(4)^2` which simplifies to

y = 45(16) so

y = 720.

Next, x = 3:

`y=45(4)^3` which simplifies to

y = 45(64) so

y = 2880