Algebra Examples

$80 = P_{0} e^{- 0.2 (4)}$

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.

$P_{0} e^{- 0.2 \cdot 4} = 80$

Step 2

Multiply $- 0.2$ by $4$ .

$P_{0} e^{- 0.8} = 80$

Step 3

Divide each term in $P_{0} e^{- 0.8} = 80$ by $e^{- 0.8}$ and simplify.

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Step 3.1

Divide each term in $P_{0} e^{- 0.8} = 80$ by $e^{- 0.8}$ .

$\frac{P_{0} e^{- 0.8}}{e^{- 0.8}} = \frac{80}{e^{- 0.8}}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $e^{- 0.8}$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{P_{0} e^{- 0.8}}{e^{- 0.8}} = \frac{80}{e^{- 0.8}}$

Step 3.2.1.2

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

$P_{0} = \frac{80}{e^{- 0.8}}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Move $e^{- 0.8}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$P_{0} = 80 e^{0.8}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$P_{0} = 80 e^{0.8}$

Decimal Form:

$P_{0} = 178.04327427 \dots$