# Exponential Growth & Decay Question !

#### ISITIEIW

##### New member
Suppose that there is initially x(not) grams of Kool-Aid powder in a glass of water. After 1 minute there are 3 grams remaining and after 3 minutes there is only 1 gram remaining. Find x(not) and the amount of Kool-Aid powder remaining after 5 minutes…

So, i set up 2 equations…

3=x(not)e^-k(1)

and 1=x(not)e^-k(3)

I know it is decaying ,but i don't know what i have to do with these equations that i made to find the value of k.

Thanks !

#### MarkFL

Staff member
Since there is no actual calculus involve in solving this problem, I am going to move the topic to our Pre-Calculus sub-forum.

You're off to a good start:

$$\displaystyle x_0e^{-k}=3$$

$$\displaystyle x_0e^{-3k}=1$$

I think what I would do next is solve both equations for $x_0$ and equate:

$$\displaystyle x_0=3e^{k}=e^{3k}$$

Next try dividing through by $e^k$ and then convert from exponential to logarithmic form.

#### ISITIEIW

##### New member
Thanks!
I got k to be 0.549306144
and got a x(not) value of 5.196152423

I got it from here !
Thanks

#### MarkFL

Staff member
Thanks!
I got k to be 0.549306144
and got a x(not) value of 5.196152423

I got it from here !
Thanks
You're welcome!

I would get in the habit of obtaining/writing exact values rather than decimal approximations. I find:

$$\displaystyle k=\ln\left(\sqrt{3} \right)$$

$$\displaystyle x_0=3\sqrt{3}$$

I realize it is possible that you found these values and simply chose to write the approximations.