Question

The population of a certain city was 122000 in 1998, and the observed relative growth rate is 3 % per year.
(a) Find a function that models the population after years, compounded continuously.
(b) Find the projected population in the year 2004.
(c) In what year will the population reach 191334?

Answer 1

for b i got 145674.38
c i got 15.224 but they are wrong so i dont know

Answer 2

Part a)
Multiply the decimal expression of the growth percentage by the current population. This number will be your coefficient for x the formula will be that resultant number multiplied by x plus the current population. The equation will be \[P(x)=ax+c\]where a is the current population times the growth rate. x represents time in years and c represents the initial population. and P(x) is the population x years later.

Part b)
Evaluate this equation at the value of x that is the desired population year minus the initial population year. Where x is:\[2004-1998\]
Part c)
Evaluate the equation to find when the population will be 191334 (P(x)=191334). To do this rearrange the population equation to find x. the rearranged equation should look like this.\[x=(P(x)-c)\div a\]
Plug in the appropriate values for P(x), a, and c and evaluate.

I am not going to just give you the answers. I hope this helps you find the answers on your own and also helps you know how to.