Solve for C 1900=2500e^(-0.02(4))+900(4)+C

$1900 = 2500 e^{- 0.02 (4)} + 900 (4) + C$

Step 1

Rewrite the equation as $2500 e^{- 0.02 \cdot 4} + 900 (4) + C = 1900$ .

$2500 e^{- 0.02 \cdot 4} + 900 (4) + C = 1900$

Step 2

Simplify each term.

Multiply $- 0.02$ by $4$ .

$2500 e^{- 0.08} + 900 (4) + C = 1900$

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

$2500 \frac{1}{e^{0.08}} + 900 (4) + C = 1900$

Combine $2500$ and $\frac{1}{e^{0.08}}$ .

$\frac{2500}{e^{0.08}} + 900 (4) + C = 1900$

Multiply $900$ by $4$ .

$\frac{2500}{e^{0.08}} + 3600 + C = 1900$

Step 3

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

Subtract $\frac{2500}{e^{0.08}}$ from both sides of the equation.

$3600 + C = 1900 - \frac{2500}{e^{0.08}}$

Subtract $3600$ from both sides of the equation.

$C = 1900 - \frac{2500}{e^{0.08}} - 3600$

Subtract $3600$ from $1900$ .

$C = - 1700 - \frac{2500}{e^{0.08}}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$C = - 1700 - \frac{2500}{e^{0.08}}$

Decimal Form:

$C = - 4007.79086596 \dots$