A function of the form \$f(x) = a \cdot b^x\$, where \$a \neq 0\$, \$b > 0\$, and \$b \neq 1\$.
A function of the form \$f(x) = a \cdot \log_b(x)\$, where \$a \neq 0\$, \$b > 0\$, and \$b \neq 1\$.
Exponential and logarithmic functions are inverse of each other. Therefore, they can be used to solve real-world problems that involve exponential growth or decay.
Note
The logarithm is used to solve for the exponent in an exponential equation. This is because the logarithm is the inverse of the exponential function.
Self review
1. A radioactive substance decays exponentially at a rate of 5% per year. If the initial amount is 100 grams, how much will remain after 10 years? 2. A population of bacteria doubles every 3 hours. If there are initially 500 bacteria, how many will there be after 12 hours? 3. A car depreciates in value by 10% each year. If the car is worth \$20,000 today, when will it be worth \$10,000?
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