Precalculus Examples

$T (10) = 65 + 145 e^{- 0.05 (10)}$

Step 1

Simplify.

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Step 1.1

Multiply $- 0.05$ by $10$ .

$T (10) = 65 + 145 e^{- 0.5}$

Step 1.2

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

$T (10) = 65 + 145 \frac{1}{e^{0.5}}$

Step 1.3

Combine $145$ and $\frac{1}{e^{0.5}}$ .

$T (10) = 65 + \frac{145}{e^{0.5}}$

Step 2

Divide each term in $T (10) = 65 + \frac{145}{e^{0.5}}$ by $10$ and simplify.

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Step 2.1

Divide each term in $T (10) = 65 + \frac{145}{e^{0.5}}$ by $10$ .

$\frac{T (10)}{10} = \frac{65}{10} + \frac{\frac{145}{e^{0.5}}}{10}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $10$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{T \cdot 10}{10} = \frac{65}{10} + \frac{\frac{145}{e^{0.5}}}{10}$

Step 2.2.1.2

Divide $T$ by $1$ .

$T = \frac{65}{10} + \frac{\frac{145}{e^{0.5}}}{10}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Simplify each term.

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Step 2.3.1.1

Cancel the common factor of $65$ and $10$ .

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Step 2.3.1.1.1

Factor $5$ out of $65$ .

$T = \frac{5 (13)}{10} + \frac{\frac{145}{e^{0.5}}}{10}$

Step 2.3.1.1.2

Cancel the common factors.

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Step 2.3.1.1.2.1

Factor $5$ out of $10$ .

$T = \frac{5 \cdot 13}{5 \cdot 2} + \frac{\frac{145}{e^{0.5}}}{10}$

Step 2.3.1.1.2.2

Cancel the common factor.

$T = \frac{5 \cdot 13}{5 \cdot 2} + \frac{\frac{145}{e^{0.5}}}{10}$

Step 2.3.1.1.2.3

Rewrite the expression.

$T = \frac{13}{2} + \frac{\frac{145}{e^{0.5}}}{10}$

Step 2.3.1.2

Multiply the numerator by the reciprocal of the denominator.

$T = \frac{13}{2} + \frac{145}{e^{0.5}} \cdot \frac{1}{10}$

Step 2.3.1.3

Combine.

$T = \frac{13}{2} + \frac{145 \cdot 1}{e^{0.5} \cdot 10}$

Step 2.3.1.4

Cancel the common factor of $145$ and $10$ .

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Step 2.3.1.4.1

Factor $5$ out of $145 \cdot 1$ .

$T = \frac{13}{2} + \frac{5 (29 \cdot 1)}{e^{0.5} \cdot 10}$

Step 2.3.1.4.2

Cancel the common factors.

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Step 2.3.1.4.2.1

Factor $5$ out of $e^{0.5} \cdot 10$ .

$T = \frac{13}{2} + \frac{5 (29 \cdot 1)}{5 (e^{0.5} \cdot 2)}$

Step 2.3.1.4.2.2

Cancel the common factor.

$T = \frac{13}{2} + \frac{5 (29 \cdot 1)}{5 (e^{0.5} \cdot 2)}$

Step 2.3.1.4.2.3

Rewrite the expression.

$T = \frac{13}{2} + \frac{29 \cdot 1}{e^{0.5} \cdot 2}$

Step 2.3.1.5

Multiply $29$ by $1$ .

$T = \frac{13}{2} + \frac{29}{e^{0.5} \cdot 2}$

Step 2.3.1.6

Move $2$ to the left of $e^{0.5}$ .

$T = \frac{13}{2} + \frac{29}{2 e^{0.5}}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$T = \frac{13}{2} + \frac{29}{2 e^{0.5}}$

Decimal Form:

$T = 15.29469456 \dots$