Question

A virus is spreading exponentially. The initial amount of people infected is 40 and it is increasing at a rate of 5% per day.

How many people will be infected with the virus after 12 days?

Round to the nearest whole number

Answer 1

I assume 40 people is the the first day?

Answer 2

If so...

...we multiply 40 by 5% for day 2.

Answer 3

**divide

not multiply

Answer 4

Anyways, 40 divided by 5% would be 800.

So then we divide 800 by 5%,

and for the rest of the days, it will be the previous day's number divided by 5%

Answer 5

Since we know that the value is increasing, and is going at a rate of 5%, we can do 100% + 5% which would leave us with 105%. Which can also be written as 1.05.

Now, we can set up our equation which is y = a ⋅ b^x

Where...
a = 40
b = 1.05
and x = 12

which would leave us with \[y = 40 \times1.05^{12}\]

Do you understand?