I need help with these two questions!!!

Question

The model y = 500(1.035)^x, indicates the value of an investment, where x is the number of whole years. What's the growth factor (the ratio from one year to the next)?

 

In the model y = 500(1.3)^x, what's the initial value (y-intercept)?

Answer 1

The model y = 500(1.035)^x, indicates the value of an investment, where x is the number of whole years. What's the growth factor (the ratio from one year to the next)?

 

Since the only increase from year to year is the compounding of 1.035 for an additional year, the growth factor is 1.035.

 

To test the premise: Take the ratio of value at 3 years divided by the value at 2 years.

 

Value at 3 years = 500(1.035)³ and Value at 2 years = 500(1.035)²

 

Taking the ratio of the two yields  500(1.035)³ ÷ 500(1.035)² = 1.035

 

In the model y = 500(1.3)^x, what's the initial value (y-intercept)?

 

For the initial value, set x=0. Any number raised to the power of zero is 1.

 

The initial value is 500*1 or 500