Help with my calculus HW?

Question

The question is If 1000 kg of raw sugar reduces to 800 kg of raw sugar during the first 10 hours, how much raw sugar will remain after another 14 hours?

I am suppose to solve this problem using equation y= y(0) e^kt
Also, this is an exponential decay/growth problem not linear.

So far I got

y=1000e^kt
800 = 1000e^k(10)
e^k = 0.8
ln(e^k) = ln 0.8
k = ln 0.8

y = 1000e^(ln 0.8)(t)

please tell me if what I did so far is right.

Answer 1

y=1000e^kt
800 = 1000*k*e^k(10)
ke^10k = 0.8

Answer 2

Close. In step 3, how did k*10 become just k?☺

Then k = (ln(.8))/10 and, after 24 hours, there should be
1000e^(((ln(.8))/10)*24) = 585.6 kg raw sugar remaining.

You're gettin' there, keep after it☺


Doug

Answer 3

520 Kg of raw sugar will remain after another 14 hours.

Plz let me know if this is the correct answer.