Calculus Examples

$y = 0.5 {(\frac{3}{4})}^{t}$

Step 1

Since $0.75$ is less than $1$ , there is an exponential decay.

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

Step 2

Setup the rate equation.

$1 - r = 0.75$

Step 3

Solve $1 - r = 0.75$ for $r$ to determine the decay factor.

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Step 3.1

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

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Step 3.1.1

Subtract $1$ from both sides of the equation.

$- r = 0.75 - 1$

Step 3.1.2

Subtract $1$ from $0.75$ .

$- r = - 0.25$

Step 3.2

Divide each term in $- r = - 0.25$ by $- 1$ and simplify.

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Step 3.2.1

Divide each term in $- r = - 0.25$ by $- 1$ .

$\frac{- r}{- 1} = \frac{- 0.25}{- 1}$

Step 3.2.2

Simplify the left side.

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Step 3.2.2.1

Dividing two negative values results in a positive value.

$\frac{r}{1} = \frac{- 0.25}{- 1}$

Step 3.2.2.2

Divide $r$ by $1$ .

$r = \frac{- 0.25}{- 1}$

Step 3.2.3

Simplify the right side.

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Step 3.2.3.1

Divide $- 0.25$ by $- 1$ .

$r = 0.25$

Step 4

Convert to a percentage.

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Step 4.1

Multiply $0.25$ by $100$ to convert to a percentage.

$0.25 \cdot 100$

Step 4.2

Simplify $0.25 \cdot 100$ .

$25 %$