The population of a city can be modeled using the formula p=100,000*10^0.02t, where t is the number of years after 2012 and P is the city's population. Which of the following equations can be used to find the number of years after 2012 that the population will triple to 300,000 ?

Answer 1

To find the number of years after 2012 that the population will triple to 300,000, we need to set 300,000 equal to the population formula and solve for t:

300,000 = 100,000*10^(0.02t)

Divide by 100,000 on both sides:
3 = 10^(0.02t)

Take the log base 10 of both sides:
log(3) = log(10^(0.02t))
log(3) = 0.02t*log(10)
log(3) = 0.02t

Divide both sides by 0.02:
log(3)/0.02 = t

Therefore, the equation to find the number of years after 2012 that the population will triple to 300,000 is:
t = log(3)/0.02.