Solve for t 100/(1+25e^(-0.095t))=70

Problem

100/(1+25*e(−0.095*t))=70

Solution

1. Isolate the denominator by multiplying both sides by 1+25*e(−0.095*t) and dividing by 70

1+25*e(−0.095*t)=100/70

2. Simplify the fraction on the right side of the equation.

1+25*e(−0.095*t)=10/7

3. Subtract 1 from both sides to begin isolating the exponential term.

25*e(−0.095*t)=10/7−7/7

25*e(−0.095*t)=3/7

4. Divide by 25 to isolate the exponential expression.

e(−0.095*t)=3/(7⋅25)

e(−0.095*t)=3/175

5. Apply the natural logarithm to both sides to remove the base e

ln(e(−0.095*t))=ln(3/175)

−0.095*t=ln(3/175)

6. Solve for t by dividing both sides by −0.095

t=ln(3/175)/(−0.095)

7. Calculate the numerical value using the properties of logarithms.

t≈(−4.066)/(−0.095)

t≈42.80

Final Answer

100/(1+25*e(−0.095*t))=70⇒t=ln(3/175)/(−0.095)≈42.80

Want more problems? Check here!