Question

In 1980, the first cd's hit the music stores. that year at a local music store 5,000 cd's were sold. each year after that, cd sales at that store increased constantly at a rate of 15,000 per year. Write a linear function for the cd's sold, C, as a function of time, t.

Answer 1

In the first year of the sale the C.D's sold = 5000.

Now next year there was an increase by 15000

C.D's sold in second year = 5000 + 15000

in third year number of cd's sold = 5000 +15000 + 15000

= 5000 + 15000*2

in fourth year it was : 5000 + 15000 * 2+ 15000 = 5000 + 15000* 3

this means in the t year number of cd's sold = 5000 + ( t-1)* 15000

let us simplify it 5000 + 15000 t - 15000

15000 t - 10000

Answer : 15000t - 10000

Answer 2

at first year 5000 compact discs were sold.

and it increased at a rate of 15000 per year in the upcoming year .

we need to linear function which mean if we graph it will get a straight line.

which is in the form of y=mx+b

where y=f(t) which means functions represented in time.

where 15000 is the slope of the equation which is increasing at this rate.

and b is the y intercept which mean from 5000 sales has been increased.

so the linear equation is

$f(t)=15000(t)+5000$