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I have a worksheet of about 24 problems and it seems to be split by two different sorts. I'm wondering if one could walk me through two so I can finish the worksheet on my own.

Write the exponential function y=20e^-0.04t in the form y=ab^t.  

Find b accurate to 5 decimal places. 

The second type of questions on the worksheet is in the following format.

Write the exponential function P=721(0.98)^t in the form P=ae^kt . 

Thank you in advance to anyone that can point me in the right direction

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$$\large (a^b)^c=a^{(b\cdot c)}$$ –  anon Sep 21 '11 at 6:36

2 Answers 2

up vote 1 down vote accepted

There is one thing you should know to do your homework and it is the following formula $$ e^{a\cdot\ln b} = b^a. $$ For example, if you have to write function $P = (0.555)^t$ in the form $P = e^{kt}$, then directly from the above formula you will get $$ (0.555)^t = e^{t\cdot \ln(0.555)}. $$ P.S. If you need to find $e^x$ with some accuracy, then it would be useful to represent $e^x$ as a series.

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Thank you, this helped me finish the homework –  jwf Sep 21 '11 at 22:55

$$ y=20e^{-0.04t} = 20 {\huge(}e^{-0.04}{\huge)}^t = ab^t\qquad\text{where }a=20\text{ and }b= e^{-0.04}. $$

(For your second question, the answer written by Ivan Polekhin suffices.)

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Thank you :) this helped –  jwf Sep 21 '11 at 22:55

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