Question

. A factory increases the production of cars annually by 8%. If presently it manufactures 211, 000 cars per year, how many cars will it manufacture per year after 4 years? Please show your work. sorry about the last post

Answer 1

Suppose that as of this year, the factory makes x cars per year this years and increases production by 8% annually. Then next year the factory will produce 108% as many cars as it produced this year, or 1.08x cars. The year after that, it will produce 108% as many cars as the previous year, or 1.08*(1.08x). The year after it will produce 108% as many cars as the previous year, or 1.08*(1.08*(1.08x)), etc

Hence, after n years the factory will be producing [(1.08)^n]x cars. Here, x = 211,000 and n = 4, so the factory will produce[1.08^4]*211000 cars, or 287063.17 cars (which we would probably round to 287063 cars)