In 2007 the population of the town of Cartersville was 24,455. The population growth can be represented by the formula P = 24,455(1.03)x, where x represents the number of years after 2007. When will the population of the town first exceed 30,000?

Question

anonymous · Answer

do you mean 1.03 to the power of x...like so$$P=24.455*(1.03)^{x}$$

anonymous · Answer

$$\log(30000/24455)/\log(1.03)$$

anonymous · Answer

yes

anonymous · Answer

do you see what i did there?

anonymous · Answer

$$P=30000=24455(1.03)^{x}=> (30000/24455)=1.03x => (\log(30000/24455)/\log(1.03)=x)$$

anonymous · Answer

oh it cut off the rest, but then then take the log of both sides and divide by log(1.03) to solve for x

anonymous · Answer

so the answer then becomes 6.91 years when it equals 30000. The population will exceed 30 000 if x>6.91 [you can click become a fan now]