Solve for t A=Pe^(rt)

$A = P e^{r t}$

Rewrite the equation as $P e^{r t} = A$ .

$P e^{r t} = A$

Divide each term by $P$ and simplify.

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Divide each term in $P e^{r t} = A$ by $P$ .

$\frac{P e^{r t}}{P} = \frac{A}{P}$

Cancel the common factor of $P$ .

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Cancel the common factor.

$\frac{P e^{r t}}{P} = \frac{A}{P}$

Divide $e^{r t}$ by $1$ .

$e^{r t} = \frac{A}{P}$

Take the natural logarithm of both sides of the equation to remove the variable from the exponent.

$\ln (e^{r t}) = \ln (\frac{A}{P})$

Expand the left side.

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Expand $\ln (e^{r t})$ by moving $r t$ outside the logarithm.

$r t \ln (e) = \ln (\frac{A}{P})$

The natural logarithm of $e$ is $1$ .

$r t \cdot 1 = \ln (\frac{A}{P})$

Multiply $r$ by $1$ .

$r t = \ln (\frac{A}{P})$

Divide each term by $r$ and simplify.

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Divide each term in $r t = \ln (\frac{A}{P})$ by $r$ .

$\frac{r t}{r} = \frac{\ln (\frac{A}{P})}{r}$

Cancel the common factor of $r$ .

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Cancel the common factor.

$\frac{r t}{r} = \frac{\ln (\frac{A}{P})}{r}$

Divide $t$ by $1$ .

$t = \frac{\ln (\frac{A}{P})}{r}$

Solve for t A=Pe^(rt)

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