A city’s population, P (in thousands), can be modeled by the equation P=130(1.03)^x , where x is the number of years after January 1, 2000. For what value of x does the model predict that the population of the city will be approximately 170,000?

A)8
B)9
C)10
D)11

Question

A city’s population, P (in thousands), can be modeled by the equation P=130(1.03)^x , where x is the number of years after January 1, 2000.  For what value of x does the model predict that the population of the city will be approximately 170,000?

A)8
		B)9
		C)10
		D)11

anonymous · Answer

P in thousands= 130(1.03)^x
170/130 = 1.03^x
$$\ln(\frac{170}{130})=xln(1.03)$$
$$\frac{\ln(\frac{170}{130})}{\ln(1.03)}=x$$
$$x \approx9$$

so the answer is B