The population of a small town has been decreasing each year.

Question

The model equation assuming modelling the decline has been variables

y= # people

x= time in years

 Equation: y= 32400(0.962)^

 

a. determine the % decrease per year

b. how long will it take for the population to decrease to half of its initial value

 

Q2: If you graph y=4^ and y=5^ on the same xy axis, for what values of x will:

• y= 4^ have greater y values?..........
• y=5^ have greater y values?..........
• Will both graphs have the same y value?

 

Answer 1

The decline rate is 1 = 0.962 = 0.038 = 3.8% per year...Q1

 

Q2: same values when exponent x = 0.

Otherwise the y values of 5^x are > than those of 4^x for x>0 but when x<0 this relationship is reversed.