Calculating Exponential Decay

Remember that there are two types of exponential functions: Remember that the criteria for each type is . . . b > 1GrowthCalculating Exponential Values0< b < 1 Decay Let's discuss . Remember that there are two types of exponential functions: Remember that the criteria for growth is . . . 0 < b < 1 Calculating Exponential Valuesdecayy = a•(b) ^{x}y = a•( ) ^{x}The common form of the equation will be used for calculations: The base, b will be expressed differently to make it more obviousthat it is less than 1 . . . where "r" is the percent decrease.Also, these problems are time based so the variable "x" is replaced by "t". So the modified equation looks like: y = a•( ) 1-r 1-r Calculating Exponential Values^{t}Let's see if you can identify the numerical values given the terms: Victor gets a truck for $17000. The value of the truck decreases by 4% each year.Find the value of the truck after 3 years. The equation for the exponential function: y = 17000•(1-0.04)^{t} or y = 17000•(0.96)^{t}Decay factor:(multiplier)Overview of terminology for growth: Initial amount: $y = a•( ) initial amount 1-r Calculating Exponential Valuesdecay factor: a single value 1-r ^{t}Percent decrease:(as a percent)What value will be put in for "t":percent decrease time % Let's see if you can calculate the value of the truck 3 years later. ^{Victor gets a truck for $17000. The value of the truck decreases by 4% each year.Find the value of the truck after 3 years.The equation for the exponential function:y = 17000•(1-0.04)t}^{}^{y = $}y = a•( ) 1-r Calculating Exponential Valuessince we are calculating money and the amount is large, round your answer to the nearest dollar. ^{t}Decay factor:(multiplier)Round your answer to the nearest dollar. A company purchased machinery in the year 1995 for $8800. Its cost depreciatedby 5% each year. What is the value of the machinery after 4 years? Initial amount: $Subtituting into the equation: y = y = a•( ) 1-r Calculating Exponential Values^{t}What value will be put in for "t":Percent decrease:(as a percent)•( Answer: $ % ) Round your answer to the nearest dollar. Ed takes a bike for $4600. The bike's value decreases by 12% each year. What is the bike's value after 5 years? y = a•( ) 1-r Calculating Exponential Values^{t}Answer: $ Round your answer to the nearest dollar. Francis started a business in the year 1991. He got $13000 profit in the first year.Each year his profit decreased by 3%. What are his profits for the tax year 1997? y = a•( ) 1-r Calculating Exponential Values^{t}Answer: $ Round your answer to the nearest dollar. A business made a profit of $17000 in 1991. Then its profits decreased by 6% eachyear for 5 years. Find its profit in the year 1996. y = a•( ) 1-r Calculating Exponential Values^{t}Answer: $ Round your answer to the nearest dollar. A company purchased machinery in the year 1990 for $7000. Its cost deprecatedat a rate of 4% per year. What is the value of the machinery after 10 years? y = a•( ) 1-r Calculating Exponential Values^{t}Answer: $ |

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