Chapter 7: Exponential Functions

Chapter 7: Exponential Functions Section 7.3: Applications of Exponential Functions 1) The value v, in dollars of a new Toyota Corolla in dollars that is t years old is modeled by the function: v(t) = 21,000(0.90)t Find the value of the Corolla in 4 years. Just plug in 4 for t, and use my calculator. I will round to 2 decimals as this is money. P(4) = 21000(0.90)4 Solution: $13,778.10 3) The number of computers infected by the spread of a virus through email can be described by the exponential function c(t)=4(1.02)t , where t is the number of minutes since the first infected e-mail was opened. Approximate the number of computers that will be infected after 6 hours (240 minutes) (round to the nearest whole number). Just plug in 240 for t. I will round to the nearest one, as a decimal number of computers would not make sense. C(240) = 4(1.02)40 Solution: 9 computers 5) The charge remaining in a battery decreases as the battery discharges. The charge C (in coulombs) after t days is given by the formula C(t)= 0.0003(0.7)t. Find the charge after 5 days. (round your answer to 5 decimal places) I will plug in 5 for t, and round per the instrutions. C(5) = 0.0003(0.7)5 My calculator gave me an answer in Scientific notation. 5.0421 x 10-5 I need to move the decimal 5 places to the left to get standard notation. This gives 0.00005421 I will round this for my answer. Solution: remaining charge .00005 coulombs 59 Chapter 7: Exponential Functions #7-10: Use the exponential growth function: P(t) = P0ert (where P0 is the initial population, r is the growth rate as a %, and t is time) to answer the following questions. 7) 100 people are in a room where a rumor is told. The number of people that have heard the rumor is growing at a rate of 25% per day. How many people will have heard the rumor after 5 days? I will replace Po with 100, and r with .25, t with 5. P(5) = 100e.25(5) P(5) = 349.03 Solution: 349 people 9) The number of daily visitors to Tumblr is currently 10 million people per day. The number is growing at a rate of 0.5% per day. How many people will visit tumbler in 30 days? (round to 2 decimals) I will replace P0 with 10, r with .005 and t with 30 P(5) = 10e.005*30 P(5) = 11.618 Solution: 11.62 million people will visit Tumblr. #11-14: Use the exponential decay function: P(t) = P0e-rt (where P0 is the initial population, r is the decay rate as a %, and t is time) to answer the following questions. 11) The number of people infected with the flu is gradually decreasing. There are currently 100 thousand people in the USA with the flu. The number of people with the flu is decreasing by 2% per day. How many people will have the flu in 30 days? P0 = 100 r = .02 t = 30 P(30) = 100e-.02*30 P(30) = 54.88116 Solution: about 55 thousand people 60 Chapter 7: Exponential Functions 13) The population of Belgium is currently 11 million. The population is decreasing by 1% per year. Estimate the population of Belgium in 10 years. P0 = 11 r = .01 t = 10 P(10) = 11e-.01*10 P(10) = 9.9532 Solution: About 10 million people 𝑟 𝑛𝑡 #15-20: Use the compound interest formula 𝐴 = 𝑃 (1 + 𝑛) to answer the following. 15) An initial deposit of $1,000 earns 4% interest compounded twice per year. How much will be in the account after 5 years? P = 1000 r = .04 n = 2 t = 5 A = 1000 (1 + .04 2∗5 ) 2 Solution: $1,218.99 17) An initial deposit of $10,000 earns 6% interest compounded quarterly. How much will be in the account after 7 years? P = 10000 r = .06 n = 4 t = 7 A = 10000 (1 + .06 4∗7 ) 4 Solution: $15,172.22 19) An initial deposit of $100,000 earns 4% interest compounded annually. How much will be in the account after 5 years? P = 100000 r = .04 n = 1 t = 5 A = 100000 (1 + .04 1∗5 ) 1 Solution: $121,665.29 61