Calculus Examples

$m (t) = {(\frac{4}{5})}^{t}$

Step 1

Since $0.8$ is less than $1$ , there is an exponential decay.

$a {(1 - r)}^{t}$

Step 2

Setup the rate equation.

$1 - r = 0.8$

Step 3

Solve $1 - r = 0.8$ for $r$ to determine the decay factor.

Tap for more steps...

Step 3.1

Move all terms not containing $r$ to the right side of the equation.

Tap for more steps...

Step 3.1.1

Subtract $1$ from both sides of the equation.

$- r = 0.8 - 1$

Step 3.1.2

Subtract $1$ from $0.8$ .

$- r = - 0.2$

Step 3.2

Divide each term in $- r = - 0.2$ by $- 1$ and simplify.

Tap for more steps...

Step 3.2.1

Divide each term in $- r = - 0.2$ by $- 1$ .

$\frac{- r}{- 1} = \frac{- 0.2}{- 1}$

Step 3.2.2

Simplify the left side.

Tap for more steps...

Step 3.2.2.1

Dividing two negative values results in a positive value.

$\frac{r}{1} = \frac{- 0.2}{- 1}$

Step 3.2.2.2

Divide $r$ by $1$ .

$r = \frac{- 0.2}{- 1}$

Step 3.2.3

Simplify the right side.

Tap for more steps...

Step 3.2.3.1

Divide $- 0.2$ by $- 1$ .

$r = 0.2$

Step 4

Convert to a percentage.

Tap for more steps...

Step 4.1

Multiply $0.2$ by $100$ to convert to a percentage.

$0.2 \cdot 100$

Step 4.2

Simplify $0.2 \cdot 100$ .

$20 %$