OpenStudy (anonymous):

Convert the given exponential function to the form indicated. Round all coefficients to four significant digits. f(t) = 2.8(1.001)^t; f(t) Qoe^kt

4 years ago
OpenStudy (anonymous):

you know that \(Q_0=2.8\) because when you replace \(t\) by \(0\) you get \(2.8\)

4 years ago
OpenStudy (anonymous):

now if \(t=1\) the left hand side is \(2.8(1.001)=2.8028\) so you can set \[2.8028=2.8e^k\] and solve for \(k\)

4 years ago
OpenStudy (anonymous):

in two steps a) divide by \(2.8\) b) take the log of both sides to find \(k\)

4 years ago
OpenStudy (anonymous):

I dont get what I take the log of exactly?

4 years ago
OpenStudy (whpalmer4):

\[2.8028 = 2.8 e^k\] \[\frac{2.8028}{2.8} = e^k\] Now take the natural log of both sides: \[\ln{\frac{2.8028}{2.8}} = \ln{e^k}\]But the natural log of e^x is just x, so \[k = \ln{2.8028/2.8} = \ln{1.001} \approx 0.000995\]

4 years ago
OpenStudy (whpalmer4):

Sorry, I formatted the last line poorly. It should be \[k = \ln{\frac{2.8028}{2.8}} = \ln{1.001} \approx 0.000995\]

4 years ago
OpenStudy (whpalmer4):

My eyes are going, the value approximately 0.0009995...

4 years ago