1. Since the sales of 8-track players are decreasing by 5.1% per year, we can say that the sales after a year are 94.9% of the sales of the previous year. For succeeding years, we just multiply the percentage a number of times corresponding to the number of years. Forming an exponential function for this we'll get:
[tex]f(x) = 390*0.949^{x} [/tex] where x is the number of years and f(x) is the number of sales.
To find the number of sales in 2013 we just plug in 3 for the value of x:
[tex]f(3) = 390*0.949^{3}=333 [/tex]
ANSWER: Emporium sold 333 8-track players in 2013.
2. The half life of Neptunium-229 is modeled by [tex]A=500* \frac{1}{2} ^{ \frac{t}{4} }[/tex] where A is the final amount and t is the time that has passed in minutes. This just means that the original amount will be multiplied by one half for every 4 minutes.
30 minutes has passed from 7:45 am to 8:15 am. Therefore, we just substitute 30 as the value of t to find the amount of Neptunium remaining by 8:15.
[tex]A=500* \frac{1}{2} ^{ \frac{30}{4} }=2.76[/tex]
ANSWER: 2.76 grams of Neptunium-229 are remaining at 8:15 am.
3. To find how much annual interest is collected over x years, we just do the same modelling as the previous items. Knowing that the initial amount that Mr. Canonaco deposited into his bank account and that the Dewey, Cheetum, & Howe Credit Union collects 6.25% annual interest per year, the equation will be as follows:
[tex]f(x)=2475.76*0.0625^{x}[/tex] where x is the number of years and f(x) is the annual interest collected.
