SOLUTION: The amount of a chemical that will dissolve in a solution increases exponentially as the (Celcius) temperature t is increased according to the model A(t)=10e^.0095t. At what tempe

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Question 251260: The amount of a chemical that will dissolve in a solution increases exponentially as the (Celcius) temperature t is increased according to the model A(t)=10e^.0095t. At what temperature will 15g dissolve?
Answer by blwinbbbles(106) About Me  (Show Source):
You can put this solution on YOUR website!
This problem is not quite defined enough so I have to give you 2 answers.
(1)
if the exponential (t) = temp. then:
15 = A(t) so:
15 = 10e^.0095(t) divide both sides by 10
1.5 = e^.0095(t) e is the inverse natural log (ln) of 1 so take the natural
of both sides... that is usually (ln) on your calculator
ln (1.5) = ln (e^.0095(t)
.40546 = .0095(t) by taking the ln of e brings the exponential down..(I am sorry that I do not remember the exact proof)
now divide both sides by .0095
42.68 = t so the temperature is 42.68 degrees Celcius
(2)
if the exponential (t) = 15 then
A(t) = 10e^.0095(15)
A(t) = 10e^0.1425
A(t) = 10(1.15315) use the e^x key on your calculator..on mine it is a second
function
A(t) = 11.5 degrees Celcius
I hope this helps