Growth and Decay
y = 21,500 • (0.85)ⁿ
A car was purchased for $21,500. Each year since, the resale value has decreased by 15%. Let n be the number of years since the purchase. Let y be the resale value of the car, in dollars. Write an exponential function showing the relationship between y and n.
y = 21,500 • (0.71)ⁿ
A car was purchased for $21,500. Each year since, the resale value has decreased by 29%. Let n be the number of years since the purchase. Let y be the resale value of the car, in dollars. Write an exponential function showing the relationship between y and n.
y = 23,500 • (0.84)ⁿ
A car was purchased for $23,500. Each year since, the resale value has decreased by 16%.Let n be the number of years since the purchase. Let y be the resale value of the car, in dollars.Write an exponential function showing the relationship between y and n.
y = 23,500 • (0.74)ⁿ
A car was purchased for $23,500. Each year since, the resale value has decreased by 26%.Let n be the number of years since the purchase. Let y be the resale value of the car, in dollars.Write an exponential function showing the relationship between y and n.
y = 2,000 • (1.0475)ⁿ
A principal of $2000 was invested at 4.75% interest, compounded annually. Let n be the number of years since the start of the investment. Let y be the value of the investment, in dollars. Write an exponential function showing the relationship between y and n.
y = 2,000 • (1.085)ⁿ
A principal of $2000 was invested at 8.5% interest, compounded annually. Let n be the number of years since the start of the investment. Let y be the value of the investment, in dollars. Write an exponential function showing the relationship between y and n.
y = 1500 • (1.13)ⁿ
At noon, to begin a study, a petri dish had 1500 bacteria cells. Each hour since, the number of cells has increased by 13%. Let n be the number of hours since the start of the study. Let y be the number of bacteria cells. Write an exponential function showing the relationship between y and n.
y = 220,000 • (1.039)ⁿ
At the beginning of a population study, a city had 220,000 people. Each year since, the population has grown by 3.9%. Let n be the number of years since start of the study. Let y be the city's population. Write an exponential function showing the relationship between y and n.
y = 220,000 • (1.057)ⁿ
At the beginning of a population study, a city had 220,000 people. Each year since, the population has grown by 5.7%. Let n be the number of years since start of the study. Let y be the city's population. Write an exponential function showing the relationship between y and n.
y = 380,000 • (1.039)ⁿ
At the beginning of a population study, a city had 380,000 people. Each year since, the population has grown by 3.9%. Let n be the number of years since start of the study. Let y be the city's population. Write an exponential function showing the relationship between y and n.
y = 380,000 • (1.063)ⁿ
At the beginning of a population study, a city had 380,000 people. Each year since, the population has grown by 6.3%. Let n be the number of years since start of the study. Let y be the city's population. Write an exponential function showing the relationship between y and n.
y = 1500 • (0.9675)ⁿ
At the beginning of an environmental study, a forest covered an area of 1500km2. Since then, this area has decreased by 3.25% each year. Let t be the number of years since the start of the study. Let y be the area that the forest covers in km2. Write an exponential function showing the relationship between y and n.
y = 1500 • (0.95)ⁿ
At the beginning of an environmental study, a forest covered an area of 1500km2. Since then, this area has decreased by 5% each year. Let t be the number of years since the start of the study. Let y be the area that the forest covers in km2. Write an exponential function showing the relationship between y and n.
y = 950 • (0.82)ⁿ
In 2006, a sample of a radioactive substance had a mass of 950 milligrams. Since then, the sample has decayed by 18% each year. Let n be the number of years since 2006. Let y be the mass of the substance in milligrams. Write an exponential function showing the relationship between y and n.
y = 950 • (0.971)ⁿ
In 2006, a sample of a radioactive substance had a mass of 950 milligrams. Since then, the sample has decayed by 2.9% each year. Let n be the number of years since 2006. Let y be the mass of the substance in milligrams. Write an exponential function showing the relationship between y and n.
y = 300,000 • (1.146)ⁿ
In 2007, a city had a population of 300,000 people. Each year since, the population has grown by 14.6%. Let n be the number of years since 2007. Let y be the city's population. Write an exponential function showing the relationship between y and n.
y = 300,000 • (1.046)ⁿ
In 2007, a city had a population of 300,000 people. Each year since, the population has grown by 4.6%. Let n be the number of years since 2007. Let y be the city's population. Write an exponential function showing the relationship between y and n.
y = 320,000 • (0.959)ⁿ
In 2007, a city had a population of 320,000 people. Each year since, the population has decreased by 4.1%. Let n be the number of years since 2007. Let y be the city's population. Write an exponential function showing the relationship between y and n.
y = 320,000 • (1.041)ⁿ
In 2007, a city had a population of 320,000 people. Each year since, the population has grown by 4.1%. Let n be the number of years since 2007. Let y be the city's population. Write an exponential function showing the relationship between y and n.
y = 320,000 • (1.044)ⁿ
In 2007, a city had a population of 320,000 people. Each year since, the population has grown by 4.4%. Let n be the number of years since 2007. Let y be the city's population. Write an exponential function showing the relationship between y and n.
y = 500 • (0.952)ⁿ
There was a sample of 500 milligrams of a radioactive substance to start a study. Since then, the sample has decayed by 4.8% each year. Let n be the number of years since the start of the study. Let y be the mass of the sample in milligrams. Write an exponential function showing the relationship between y and n.
y = 500 • (0.925)ⁿ
There was a sample of 500 milligrams of a radioactive substance to start a study. Since then, the sample has decayed by 7.5% each year. Let n be the number of years since the start of the study. Let y be the mass of the sample in milligrams. Write an exponential function showing the relationship between y and n.
y = 1900 • (1.11)ⁿ
To begin a bacteria study, a petri dish had 1900 bacteria cells. Each hour since, the number of cells has increased by 11%. Let n be the number of hours since the start of the study. Let y be the number of bacteria cells. Write an exponential function showing the relationship between y and n.
y = 1900 • (1.15)ⁿ
To begin a bacteria study, a petri dish had 1900 bacteria cells. Each hour since, the number of cells has increased by 15%. Let n be the number of hours since the start of the study. Let y be the number of bacteria cells. Write an exponential function showing the relationship between y and n.
