Calculus Examples

$100 e^{- 0.0001 \cdot 1000} + 150$

Step 1

Simplify each term.

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Step 1.1

Multiply $- 0.0001$ by $1000$ .

$100 e^{- 0.1} + 150$

Step 1.2

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

$100 \frac{1}{e^{0.1}} + 150$

Step 1.3

Combine $100$ and $\frac{1}{e^{0.1}}$ .

$\frac{100}{e^{0.1}} + 150$

Step 2

To write $150$ as a fraction with a common denominator, multiply by $\frac{e^{0.1}}{e^{0.1}}$ .

$\frac{100}{e^{0.1}} + \frac{150 e^{0.1}}{e^{0.1}}$

Step 3

Combine the numerators over the common denominator.

$\frac{100 + 150 e^{0.1}}{e^{0.1}}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{100 + 150 e^{0.1}}{e^{0.1}}$

Decimal Form:

$240.48374180 \dots$