4e^(-.03x)-7=13
adding 7 __ 4e^(-.03x)=20
dividing by 4 __ e^(-.03x)=5
taking natural log __ -.03 x = ln(5)
dividing by -.03 __ x = ln(5) / -.03
1000
To solve the equation 4e^(-0.03x) - 7 = 13 for x, we will follow these steps:
Step 1: Add 7 to both sides of the equation to isolate the exponential term:
4e^(-0.03x) = 20
Step 2: Divide both sides of the equation by 4 to isolate the exponential term:
e^(-0.03x) = 5
Step 3: Take the natural logarithm (ln) of both sides of the equation to remove the exponential term. The natural logarithm is the inverse function of the exponential function e^x:
ln(e^(-0.03x)) = ln(5)
Step 4: Apply the property of logarithms, ln(e^x) = x, to simplify the left side of the equation:
-0.03x = ln(5)
Step 5: To solve for x, divide both sides of the equation by -0.03:
x = ln(5) / -0.03
Step 6: Calculate the numerical value of x using a calculator:
x ≈ -72.46
Therefore, the solution to the equation 4e^(-0.03x) - 7 = 13 is approximately x = -72.46.