can i get help solving a word problem

Question

the volume was increasing exponentially.  One minute after the little bang, the volume was 10 cubic kilometers, and three minutes after the little bang, the volume was 30 cubic kilometers. Solve for k.

 

Answer 1

exponential growth is of the form

y = ab^x

So, using your points, we have

a*b¹ = 10

a*b³ = 30

Divide, and you get

b² = 3

That makes a = 10/√3

y = 10/√3 * 3^x/2 = 10*3^(x-1)/2

I have no idea what k is in your question, but if you want a function of the form y = ae^kx then just recall that 3 = e^ln3 and you could write this as

y = 10/√3 e^{ln3/2 x}

which would make k = ln3/2