1) "Solve the equation: The price of a new car is $28,000 and it depreciates 9% each year. How much is the car worth in 6 years?"
I THINK #1 is as follows...
y = 28,000(1+/-0.09)^6
y = 28,000(+/-1.09)^6
y = 28,000(1.678)
y = 46,984
And this looks completely wrong to me.
2) "Solve the equation: A population of 175 snails is increasing at an annual rate of 12%. At this rate, how long will it take for the population of snails to reach 315?"
I have absolutely no idea.
I know that I should apply the formulas y = ae^+/-kt and y = a(1+/-r)^t, but I'm not quite sure for which type of problem uses which formula. I do believe that y = a(1+/-r)^t is used for money, but again, I'm just stuck on how to do these. Thanks in advance to anyone who'll tackle these.
After N years the population is:
P(N) = 175 (1+0.12)^N.
If the population after N years is 315 then we hav:
315 = 175 (1.12)^N
which we have to solve.
rearranging this gives:
(1.12)^N = 315/175 = 1.8
Now take logs:
N log(1.12) = log(1.8),
so:
N = log(1.8)/log(1.12) ~= 5.19 years.
RonL