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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.

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Sophie2917
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
JeanaShupp

Answer: [tex]f(h)=500(1.02)^{24h}[/tex]

Step-by-step explanation:

The exponential growth equation is given by :-

[tex]f(x)=A(1+r)^x[/tex], 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 =[tex]\dfrac{48\%}{24}=2\%[/tex] 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

[tex]f(h)=500(1+0.02)^{24h}\\\\\Rightarrow\ f(h)=500(1.02)^{24h}[/tex]

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