Question

The temperature of Andrea's coffee is given by the equation y = 108e-0.32t + 72 in degrees Fahrenheit t minutes after she pours it.

Andrea prefers her coffee at 115 oF.

How long should she wait before drinking her coffee? Round your answer to the nearest tenth of a minute.

Answer 1

Two thing I need clearification: 1, y is the temperature in degree F. 2, the correct form of the equation is\[y=108e ^{-0.32t}+72\]

Answer 2

yes thats the correct form of the equation. and thats the exact question, so im not sure if y is the temperature in degree, but i assume it is

Answer 3

Ok, so y=115, right?

Answer 4

It is stated in the question

Answer 5

oh yeah nvm

Answer 6

assuming that y is indeed the temp, otherwise we are screwed

Answer 7

so now what?

Answer 8

so 108*e(t)=115-72=43, where e(t) denotes the exponential part of the equation

Answer 9

\[e(t)=\frac{ 43 }{ 108 }\]

Answer 10

\[\ln (e(t))=\ln(\frac{ 43 }{ 108 })\]

Answer 11

\[\ln(e(t))=-0.32t\]

Answer 12

\[-0.32t=ln(\frac{ 108 }{ 43 })\]

Answer 13

\[t=\frac{ \ln(\frac{ 108 }{ 43 }) }{ -0.32 }\]

Answer 14

put the RHS into calculator and that's your answer

Answer 15

I am soooo sorry! you should have noticed that I have switched places!

Answer 16

explanation\[t=\frac{ \ln(\frac{ 43 }{ 108 }) }{ -0.32 }=\frac{- \ln(\frac{ 43 }{ 108 }) }{ 0.32 }=\frac{ \ln(\frac{ 108 }{ 43 }) }{ 0.32 }\]

Answer 17

that should be you REALLY CORRECT answer