Practice Exponential Function in Math
Use these practice problems to test your method after reviewing the concept explanation and worked examples.
Quick Recap
An exponential function has the form where , . The variable is in the exponent, not the base.
Growth (or decay) that multiplies by a constant factor repeatedly.
Showing a random 20 of 50 problems.
Example 1
challengeTwo species of bacteria start with the same population. Species A doubles every hours, Species B triples every hours. After how many hours do their populations match again, other than at ? Express the smallest positive answer.
Example 2
hardA bacterial culture grows from to in hours. Assuming exponential growth, find the doubling time.
Example 3
easyWhat is the initial value in ?
Example 4
mediumWhat is the range of ?
Example 5
easyIs or the exponential function?
Example 6
mediumThe population of a town grows from to in years exponentially. Find the annual growth rate.
Example 7
easyEvaluate .
Example 8
hardFor what value of does pass through ?
Example 9
easyA bacteria population starts at 500 and doubles every 3 hours. Write an exponential model and find the population after 9 hours.
Example 10
mediumSolve .
Example 11
challengeIf and , find .
Example 12
mediumA quantity halves every years from grams. How much remains after years?
Example 13
easyWhat is the domain of ?
Example 14
mediumSolve .
Example 15
mediumSimplify .
Example 16
challengeSolve .
Example 17
mediumA radioactive substance has a half-life of 10 years. If the initial amount is 200 g, how much remains after 30 years?
Example 18
mediumIdentify the growth factor of .
Example 19
mediumSolve .
Example 20
mediumSolve .