A culture contains 10,000 bacteria with the population increasing exponentially the culture contains 15,000 bacteria after six hours. HELP!!!

Step-by-step explanation:

Hi there,

a)

Notice the starting amount in an exponential equation, like in this one, is y₀. The culture starts with 10,000 bacteria, so this is our y₀ ! The y₀ value always remains constant for every exponential equation.

Now, they tell us the culture reaches 15,000 bacteria after 6 hours. So, this is the y-value at t=6. From this, we can solve for k, and finally obtain this exponential equation:

Divide both sides by 10,000 to isolate the exponential term:

Now, you have to take the natural logarithm of both sides, as this is the inverse function of the e base:

Use a calculator to determine ln(1.5), and now divide both sides by 6 to isolate k:

I would recommend keeping k to more digits like above, unless your prompt says specifically how many digits to keep. This is because exponential values can change significantly even if you change the exponential term slightly.

Now, we have everything to build the equation!

b)

As for part b, they simply ask to equate:

 which is the only difference. y₀ is still the same. To do this, all you have to do is raise e to the k power:

Now you can solve part c on your own!

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