Solve the exponential equation for t. Round your answer to three decimal places if necessary.
e^(0.08t)=4
Please show work
To solve the exponential equation e^(0.08t) = 4 for t, we can take the natural logarithm (ln) of both sides:
ln(e^(0.08t)) = ln(4)
Using the logarithmic property ln(e^x) = x, we get:
0.08t = ln(4)
Now, we can isolate the variable t by dividing both sides of the equation by 0.08:
t = ln(4) / 0.08
Using a calculator, we can now evaluate this expression:
t ≈ 10.989
Rounded to three decimal places, the solution to the equation e^(0.08t) = 4 is t ≈ 10.989.
To solve the exponential equation e^(0.08t) = 4 for t, we need to apply the natural logarithm (ln) to both sides of the equation. The natural logarithm undoes the exponential function.
Step 1: Take the natural logarithm (ln) of both sides of the equation:
ln(e^(0.08t)) = ln(4)
Step 2: Apply the logarithmic property of exponents:
0.08t * ln(e) = ln(4)
Step 3: Simplify:
0.08t = ln(4)
Step 4: Divide both sides of the equation by 0.08:
t = ln(4) / 0.08
Now, using a calculator, evaluate the right-hand side of the equation to find an approximate value for t.
t ≈ ln(4) / 0.08
t ≈ 0.693 / 0.08
t ≈ 8.663
Therefore, the solution to the exponential equation e^(0.08t) = 4, rounded to three decimal places, is t ≈ 8.663.
Come on, guy. Surely by now you can do this one?
e^.08t = 4
.08t = ln 4
t = ln4/.08 = 17.329