Answer:
[tex] n(t=2) = 2 e^{1.386294361(2)}=32 grams [/tex]
So then after 2 hours we will have 32 grams.
Step-by-step explanation:
For this case we have the followin exponential model:
[tex] n(t) = n e^{rt} [/tex]
n(t) is the quantity after t hours, n is the original quantityand t represent the hours and r the rate constant.
For this case we know that n(0) = 2 grams and n(3) = 128 grams and we want to find n(2)=?
From the initial condition we know that n = 2, and we have the model like this:
[tex] n(t) = 2 e^{rt} [/tex]
Now if we apply the other conditionn(3) = 128 we got:
[tex] 128 = 2 e^{3r}[/tex]
If we divide both sides by 2 we got:
[tex] 64= e^{3r}[/tex]
If we apply natural log for both sides we got:
[tex] ln(64) = 3r [/tex]
[tex] r = \frac{ln(64)}{3}=1.386294361[/tex]
And our model is this one:
[tex] n(t) = 2 e^{1.386294361t} [/tex]
And if we replace t = 2 hours we got:
[tex] n(t=2) = 2 e^{1.386294361(2)}=32 grams [/tex]
So then after 2 hours we will have 32 grams.
