# Solve for C 1900=2500e^(-0.02(4))+900(4)+C 1900=2500e-0.02(4)+900(4)+C
Rewrite the equation as 2500e-0.02⋅4+900(4)+C=1900.
2500e-0.02⋅4+900(4)+C=1900
Simplify each term.
Multiply -0.02 by 4.
2500e-0.08+900(4)+C=1900
Rewrite the expression using the negative exponent rule b-n=1bn.
25001e0.08+900(4)+C=1900
Combine 2500 and 1e0.08.
2500e0.08+900(4)+C=1900
Multiply 900 by 4.
2500e0.08+3600+C=1900
2500e0.08+3600+C=1900
Move all terms not containing C to the right side of the equation.
Subtract 2500e0.08 from both sides of the equation.
3600+C=1900-2500e0.08
Subtract 3600 from both sides of the equation.
C=1900-2500e0.08-3600
Subtract 3600 from 1900.
C=-1700-2500e0.08
C=-1700-2500e0.08
Convert the decimal exponent to a fractional exponent.
Convert the decimal number to a fraction by placing the decimal number over a power of ten. Since there are 2 numbers to the right of the decimal point, place the decimal number over 102 (100). Next, add the whole number to the left of the decimal.
C=-1700-2500e8100
Cancel the common factor of 8 and 100.
Factor 4 out of 8.
C=-1700-2500e4(2)100
Cancel the common factors.
Factor 4 out of 100.
C=-1700-2500e4⋅24⋅25
Cancel the common factor.
C=-1700-2500e4⋅24⋅25
Rewrite the expression.
C=-1700-2500e225
C=-1700-2500e225
C=-1700-2500e225
C=-1700-2500e225
The result can be shown in multiple forms.
Exact Form:
C=-1700-2500e225
Decimal Form:
C=-4007.79086596…
Solve for C 1900=2500e^(-0.02(4))+900(4)+C

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