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Algebra/Write the function in the form

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Question
Write the function in the form P=P0e^kt

P=15(2.5)^t

P=

Answer
Note that in mathematices, exponets are calculated first, so what is written is really
P = P0(e^k)t, but we both know that this is not what is meant.
The equation is really P = P0*e^(kt).


It is known that b*ln(a) = ln(a^b).
Taking the exponential of each side gives e^(b*ln(a)) = e^ln(a^b).
Taking the exponential of a ln() cancels, leaving e^(b*ln(a)) = a^b.
This gives a^b = e^(b*ln(a)).

This means that 2.5^t = e^(t*ln(2.5)).

From here, it can be seen that if P0 = 15 and k = ln(2.5), we get P = P0e^(kt).

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Scott A Wilson

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Any algebraic question you've got. That includes question that are linear, quadratic, exponential, etc.

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I have solved story problems, linear equations, parabolic equations. I have also solved some 3rd order equations and equations with multiple variables.

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MS at math OSU in mathematics at OSU, 1986. BS at OSU in mathematical sciences (math, statistics, computer science), 1984.

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