Solve for P0 60=P_0e^(-0.2(7))

$60 = P_{0} e^{- 0.2 (7)}$

Step 1

Since $P_{0}$ is on the right side of the equation, switch the sides so it is on the left side of the equation.

$P_{0} e^{- 0.2 \cdot 7} = 60$

Step 2

Multiply $- 0.2$ by $7$ .

$P_{0} e^{- 1.4} = 60$

Step 3

Divide each term in $P_{0} e^{- 1.4} = 60$ by $e^{- 1.4}$ and simplify.

Divide each term in $P_{0} e^{- 1.4} = 60$ by $e^{- 1.4}$ .

$\frac{P_{0} e^{- 1.4}}{e^{- 1.4}} = \frac{60}{e^{- 1.4}}$

Simplify the left side.

Cancel the common factor of $e^{- 1.4}$ .

Cancel the common factor.

$\frac{P_{0} e^{- 1.4}}{e^{- 1.4}} = \frac{60}{e^{- 1.4}}$

Divide $P_{0}$ by $1$ .

$P_{0} = \frac{60}{e^{- 1.4}}$

Simplify the right side.

Move $e^{- 1.4}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$P_{0} = 60 e^{1.4}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$P_{0} = 60 e^{1.4}$

Decimal Form:

$P_{0} = 243.31199801 \dots$