Solve the exponential equation. Give the answer correct to 3 decimal places. $57 = \frac { 77 } { 1 + 4 e ^ { - 0.1 x } }$
A)-2.434
B)-0.877
C)5.315
D)-0.532
E)24.336

Question

Quizplus · Accepted Answer

To solve the equation, first isolate the exponential term: $1 + 4e^{-0.1x} = \frac{77}{57}$. Simplify and solve for $e^{-0.1x}$, then take the natural logarithm to solve for $x$. The solution is approximately 24.336.

Solve the Exponential Equation 57=771+4e−0.1x57 = \frac { 77 } { 1 + 4 e ^ { - 0.1 x } }57=1+4e−0.1x77​

Solve the Exponential Equation $57 = \frac { 77 } { 1 + 4 e ^ { - 0.1 x } }$