Solve for I I(10)=8400-6500e^(-0.004(10))

$I (10) = 8400 - 6500 e^{- 0.004 (10)}$

Step 1

Simplify.

Multiply $- 0.004$ by $10$ .

$I (10) = 8400 - 6500 e^{- 0.04}$

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

$I (10) = 8400 - 6500 \frac{1}{e^{0.04}}$

Combine $- 6500$ and $\frac{1}{e^{0.04}}$ .

$I (10) = 8400 + \frac{- 6500}{e^{0.04}}$

Move the negative in front of the fraction.

$I (10) = 8400 - \frac{6500}{e^{0.04}}$

Step 2

Divide each term in $I (10) = 8400 - \frac{6500}{e^{0.04}}$ by $10$ and simplify.

Divide each term in $I (10) = 8400 - \frac{6500}{e^{0.04}}$ by $10$ .

$\frac{I (10)}{10} = \frac{8400}{10} + \frac{- \frac{6500}{e^{0.04}}}{10}$

Simplify the left side.

Cancel the common factor of $10$ .

Cancel the common factor.

$\frac{I \cdot 10}{10} = \frac{8400}{10} + \frac{- \frac{6500}{e^{0.04}}}{10}$

Divide $I$ by $1$ .

$I = \frac{8400}{10} + \frac{- \frac{6500}{e^{0.04}}}{10}$

Simplify the right side.

Simplify each term.

Divide $8400$ by $10$ .

$I = 840 + \frac{- \frac{6500}{e^{0.04}}}{10}$

Multiply the numerator by the reciprocal of the denominator.

$I = 840 - \frac{6500}{e^{0.04}} \cdot \frac{1}{10}$

Cancel the common factor of $10$ .

Move the leading negative in $- \frac{6500}{e^{0.04}}$ into the numerator.

$I = 840 + \frac{- 6500}{e^{0.04}} \cdot \frac{1}{10}$

Factor $10$ out of $- 6500$ .

$I = 840 + \frac{10 (- 650)}{e^{0.04}} \cdot \frac{1}{10}$

Cancel the common factor.

$I = 840 + \frac{10 \cdot - 650}{e^{0.04}} \cdot \frac{1}{10}$

Rewrite the expression.

$I = 840 + \frac{- 650}{e^{0.04}}$

Move the negative in front of the fraction.

$I = 840 - \frac{650}{e^{0.04}}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$I = 840 - \frac{650}{e^{0.04}}$

Decimal Form:

$I = 215.48686455 \dots$