Calculus Examples

$T (20) = - 7 + 29 e^{- 0.05 (20)}$

Step 1

Simplify.

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Multiply $- 0.05$ by $20$ .

$T (20) = - 7 + 29 e^{- 1}$

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$T (20) = - 7 + 29 \frac{1}{e}$

Combine $29$ and $\frac{1}{e}$ .

$T (20) = - 7 + \frac{29}{e}$

Step 2

Divide each term in $T (20) = - 7 + \frac{29}{e}$ by $20$ and simplify.

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Divide each term in $T (20) = - 7 + \frac{29}{e}$ by $20$ .

$\frac{T (20)}{20} = \frac{- 7}{20} + \frac{\frac{29}{e}}{20}$

Simplify the left side.

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Cancel the common factor of $20$ .

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Cancel the common factor.

$\frac{T \cdot 20}{20} = \frac{- 7}{20} + \frac{\frac{29}{e}}{20}$

Divide $T$ by $1$ .

$T = \frac{- 7}{20} + \frac{\frac{29}{e}}{20}$

Simplify the right side.

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Simplify each term.

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Move the negative in front of the fraction.

$T = - \frac{7}{20} + \frac{\frac{29}{e}}{20}$

Multiply the numerator by the reciprocal of the denominator.

$T = - \frac{7}{20} + \frac{29}{e} \cdot \frac{1}{20}$

Multiply $\frac{29}{e}$ by $\frac{1}{20}$ .

$T = - \frac{7}{20} + \frac{29}{e \cdot 20}$

Move $20$ to the left of $e$ .

$T = - \frac{7}{20} + \frac{29}{20 e}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$T = - \frac{7}{20} + \frac{29}{20 e}$

Decimal Form:

$T = 0.18342518 \dots$