Find the Constant of Variation and state the equation.

Question

I have tried to figure out what to do for quite a while but I still don't get it. I would greatly appreciate help. I don't know what to do, much less the answer for this word problem:

"A micro-organism grows at an exponential rate. At noon there are 10 of the organisms in a beaker. At 1:00 there are 5000 organisms in the beaker. First, solve for the constant of variation and then state the equation that models this growth behavior."

I need to figure this out soon. Thanks!

Answer 1

Basic idea is y = ab^t

You have to solve for a and b.

Our first situation is 10 organisms at t = 0. So 10 = ab^0. What must a be?

Now you have y = 10b^t To find out b, plug in the next situation in which y = 5000 and t = 1

That tells you what b is and then you can write the formula.