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Review for Exponential Growth Credit will not be given for rounding errors or adding commas when the instructions state not to add them. Remember to read the instructions and round accordingly. Calculating Exponential Values Calculating Remember that the criteria for growth is . . . Quiz for exponential functions: Calculating Exponential Values b > 1 growth y = a•( )x The common form of the equation will be used for calculations: The base, 'b' can be expressed differently... b may be 2 if doubling, b may be 3 if tripling, etc. . . . If the problem calls for a percent increase, the equation will be like above where "r" is the percent increase. So the general equation looks like: y = a•(b)x y = a•( ) 1+r Calculating Exponential Values b x Where 'b' is the growth factor Let's see if you can identify the numerical values given the terms: The cost of a movie ticket is $8, which increases by 3% each year.Find the cost of the ticket after 7 years. Here is the equation for the exponential function: y = 8•(1+0.03)t or y = 8•(1.03)t Growth factor:(a single value) Overview of terminology for growth: Initial amount: $ y = a•( ) initial amount 1+r Calculating Exponential Values growth factor: a single value 1+r x Percent increase:(as a percent) What value will be put in for "x": percent increase time % Let's see if you can calculate the cost of the movie ticket 7 years later. The cost of a movie ticket is $8, which increases by 3% each year.Find the cost of the ticket after 7 years. Here is the equation for the exponential function: y = 8•(1+0.03)x y = 8•(1.03)7 y = $ y = a•( ) 1+r since we are calculating money roundyour answer to the nearest penny. Calculating Exponential Values x Growth factor:(one value) Round your answer to the nearest dollar. Rents in a particular area are increasing by 4% every year. Predict what therent of the apartment would be after 5 years, if its rent is $400 per month now. Initial amount: $ Subtituting into the equation: y = y = a•( ) 1+r Calculating Exponential Values x What value will be put in for "x": Percent increase:(as a percent) •( Answer: $ ) % The population of the United States was about 250 million in 2003,and is growing exponentially at a rate of about 0.7% (be careful changing this percent) per year. What will be its population in the year 2015? Round your answer to the nearest million. y = a•( ) 1+r Calculating Exponential Values x Answer: million Round your answer to the nearest dollar. A business man made a profit of $15,153 in 1990. The profit increasedby 2% per year for the next 10 years. Identify an exponential growthmodel for the profit and find the annual profit in the year 2000. Subtituting into the equation: y = y = a•( ) For large numbers, include commas where appropriate 1+r Calculating Exponential Values x initial amount Answer: $ •( growth factor: a single value 1+r ) time Round your answer to the nearest integer. For large numbers, include commas where appropriate. An initial population of 456 starfish triples each year for 4 years. What is the population after 4 years? y = a•( ) b Calculating Exponential Values x Answer: Some of the new 'super' bacteria can split into two identical cells (double) every 30 minutes.
Suppose 5 of these "super" bacteria were to land in a cut on your arm around noon. If your body is unable to resist / kill the bacteria, how many of these bacteria will be in your system by midnight?
(remember to consider the 30 minute intervals) Number of bacteria by midnight: (Please round to the nearest million) Calculating Exponential Values million Suppose you invested $50 in a savings account that pays 3.5% each year.
How much would you have in your account after 1 year? 5 years? 10 years? 20 years? (Remember to round money accordingly) 20 years? 5 years? 10 years? 1 year? Calculating Exponential Values $ $ $ $ |