Question

Exponential growth
the formulas for growth
y=a(1+r)^x and y=a(e^kx)
where
y=result
a=starting amt.
r=rate
x=time elapsed
k=constant
any explanation when to use one of these???

Answer 1

here is an example

Answer 2

Example: 2 months ago you had 3 mice, you now have 18.

Mice
Assuming the growth continues like that

What is the "k" value?
How many mice 2 Months from now?
How many mice 1 Year from now?


Start with the formula:

y(t) = a × ekt

We know a=3 mice, t=2 months, and right now y(2)=18 mice:

18 = 3 × e2k

Now some algebra to solve for k:

Divide both sides by 3: 6 = e2k

Take the natural logarithm of both sides: ln(6) = ln(e2k)

ln(ex)=x, so: ln(6) = 2k

Rearrange: k = ln(6)/2


Now, we want to know the population in 2 more months (at t=4 months), and in 1 year from now (t=14 months):



y(4) = 3 e(ln(6)/2)×4 = 108

y(14) = 3 e(ln(6)/2)×14 = 839,808



That's a lot of mice! I hope you will be feeding them properly.