## JamenS 3 years ago HELP PLZ The amount of freight transported by rail in the United States was about 580 billion ton-miles in 1960 and has been increasing at a rate of 2.32% per year since then. (a) Write a function representing the amount of freight, in billions of ton-miles, transported annually (1960 = year 0). (b) Graph the function. (c) In what year would you predict that the number of ton-miles would have exceeded or would exceed 1 trillion (1000 billion)?

1. nphuongsun93

2.32% = 0.0232 f(t) = 580(1+0.0232)^t

2. JamenS

You want 580 x 10^9 (1.0232)^N to be one trillion, i.e. 10^12. Thus 580 (1.0232)^N = 10^3 1.0232^N = 1000 / 580 = 1. 17241 Take logs of both sides. N log(1.0232) = log (1.17241) N = 0.06944/0.00995 N = 6.979 (years) So it needs 7 full years from 1960 to reach one trillion. So it occurs in 1967

3. JamenS

?

4. nphuongsun93

ya, thats correct

5. nphuongsun93

think you have to do the log calculation again, i got 23.7 years

6. nphuongsun93

ah 1000/580 = 1.724