What is the answer to solvefor t,A=A_{0}e^{kt} ?

The answer to solvefor t,A=A_{0}e^{kt} is t=(ln(A/(A_{0)}))/k

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solvefor t,A=A_{0}e^{kt}

solve for

t, A = A_{0} e^{k t}

t = \frac{ln ( \frac{A}{A _{0}} )}{k}

Solution steps

A = A_{0} e^{k t}

Switch sides

A_{0} e^{k t} = A

Divide both sides by

A_{0}

e^{k t} = \frac{A}{A _{0}}

Apply exponent rules

k t = ln (\frac{A}{A _{0}})

Solve

k t = ln (\frac{A}{A _{0}}) : t = \frac{ln ( \frac{A}{A _{0}} )}{k}

t = \frac{ln ( \frac{A}{A _{0}} )}{k}

9^{5 x + 7} = \frac{1}{729}

x, 0 = e^{- x}

(3^{x})^{2} = 81

6^{2 x + 1} = 5^{x}

\frac{1}{81} 3^{5 x + 1} = 81

What is the answer to solvefor t,A=A_{0}e^{kt} ?
The answer to solvefor t,A=A_{0}e^{kt} is t=(ln(A/(A_{0)}))/k