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HELP i have a exponential functions nd i need to know if my word problem is solve able pls

The Population of salmonella
doubles in size every 25 hours.
There are about 1.35 million
infections every year, determine
how many bacteria is present
every year.

1 Answer

6 votes

Yes, this word problem is solvable using exponential functions.

To solve this problem, we need to use the formula for exponential growth:

P(t) = P0 * e^(rt)

where P(t) is the population after t hours, P0 is the initial population, r is the growth rate, and e is the mathematical constant approximately equal to 2.71828.

In this problem, we are given that the population doubles in size every 25 hours. This means that the growth rate is 1/25, since the population is multiplying by 2 each time.

We are also given that there are about 1.35 million infections every year. Since there are 365 days in a year, this means there are about 1.35 million/365 = 3699.18 infections per day.

We can now use this information to find the initial population:

P0 = 3699.18 / e^(1/25 * 24 * 365)

P0 ≈ 2135.05

So the initial population is about 2135.05 bacteria.

To find the population after one year, we can use the formula again:

P(365 * 24) = 2135.05 * e^(1/25 * 24 * 365)

P(365 * 24) ≈ 3.89 x 10^18

Therefore, there are approximately 3.89 x 10^18 bacteria present after one year.

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