Question

A certain species of bacteria grows at a rate of 48% per day. There are 500 initially, therefore the equation is y = 500(1.48)t. Write an equation for the amount of bacteria in terms of hours.

Answer 1

The bacteria would grow at a rate of 2% per hour. ( 48% divided by 24 hours in a day = 2%). So, the equation would be y=500(1.02)t

Answer 2

Answer:
`f(h)=500(1.02)^(24h)`

Explanation:

The exponential growth equation is given by :-

`f(x)=A(1+r)^x`, where A is the initial amount, r is the rate of growth and x is the time period.

Given: The initial amount = 500

Rate of growth = 48% per day.

Since 1 day = 24 hours

Then , the rate of growth =
`(48\%)/(24)=2\%` per hour =0.02

Time t=24h, where h is the number of hours

Now, the equation for the amount of bacteria in terms of hours will be

`f(h)=500(1+0.02)^(24h)\\\\\Rightarrow\ f(h)=500(1.02)^(24h)`