Question

in 1980 there were about 170 million vehicles and about 227 million people in the United States. The number of vehicles grows at 4% a year while the pop grows at 1% per year.when was there on average, one vehicle per person?

Answer 1

1980
veh = 170*(1.04)^years
popul = 227*(1.01)^years

So when does 170*(1.04)^years = 227*(1.01)^years ?
taking logs of both sides
years * 2.2304489214 + 0.0170333393 = years * 2.3560258572 + 0.0043213738
years * 2.2474822607 = years * 2.360347231
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Figured I'd try this by trial and error.
In 1990
vehicles = 251.6415 people = 250.749

Answer 2

Seems as if I'm having problems taking the logarithm of a function of the type
m * (n ^ years)

Answer 3

veh = 170*(1.04)^years
popul = 227*(1.01)^years

So, we make these equal to each other
170*(1.04)^years = 227*(1.01)^years

227/170 = (1.04)^years / (1.01)^years

Taking logs of both sides
log (227/170) = years * log (1.04/1.01)

0.1255769358 = years * (0.0127119655)
years = 0.1255769358 / 0.0127119655
= 9.8786403767 years

Yes, it's just that simple.