I know this is an exponential function based on the fact the f(x) multiplies. But how do I get an equation from the table? I will report links and fake answers. Also please include an explanation because I am trying to learn myself.

An exponential function is defined by the formula f(x) = ax, where the input variable x occurs as an exponent. The exponential curve depends on the exponential function and it depends on the value of the x.

Step 1: Take the natural log of both sides:

Step 2: Simplify the left side of the above equation using Logarithmic Rule 3:

Step 3: Simplify the left side of the above equation: Since Ln(e)=1, the equation reads

Ln(80) is the exact answer and x=4.38202663467 is an approximate answer because we have rounded the value of Ln(80)..

Check: Check your answer in the original equation.

Example 2: Solve for x in the equation tex2html_wrap_inline133

Step 1: Isolate the exponential term before you take the common log of both sides. Therefore, add 8 to both sides: tex2html_wrap_inline135

Step 2: Take the common log of both sides:

Step 3: Simplify the left side of the above equation using Logarithmic Rule 3:

Step 4: Simplify the left side of the above equation: Since Log(10) = 1, the above equation can be written

Step 5: Subtract 5 from both sides of the above equation:

is the exact answer. x = -3.16749108729 is an approximate answer..

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