y=6.72(1.014^x) models the worlds population y in billions of people x is years after thr year 2000 find thr year in which the population is 16 billion

Question

Formula A=P(1+r/n)n*t

Answer 1

You don't need to use the other formula since they provide you with an equation for this particular problem.  The formula will come in handy when they just give you information but not an equation to use.

 

since y = 6.72(1.014^x) represents the population in billions and we want the population to be 16 billion, we can replace the y with 16, and then try to solve for x using logs.

 

16 = 6.72(1.014^x)       divide by 6.72

(16/6.72) = 1.014^x      take the log of both sides

log (16/6.72) = log (1.014^x)          bring the power down (this is why logs are useful for these problems)

log (16/6.72) = x*log(1.014)         and divide by log(1.014)

x = log(16/6.72) / log(1.014)

x = 62.3971...

Remember that's years after 2000, so it'll be sometime during 2062.

 

If you plug the x value back into the original equation (as a decimal would be easiest), you should get about 16 for y.