Convert the given e… - QuestionCove
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