Exponential function models the annual rate of increase. Find the monthly and quarterly rates​

9514 1404 393

  1.  monthly: 0.25%; quarterly: 0.75%

  2.  monthly: ≈ 0.45833%; quarterly: 1.375%

Step-by-step explanation:

In each case, the base of the exponential term is the annual growth factor. The annual growth rate (interest rate) is ...

  growth rate = growth factor - 1

Then the monthly rate is ...

  monthly rate = growth rate/12

and the quarterly rate is ...

  quarterly rate = growth rate/4

__

1. monthly rate = (1.03 -1)/12 = 0.03/12 = 0.0025 = 0.25%

  quarterly rate = (1.03 -1)/4 = 0.03/4 = 0.0075 = 0.75%

__

2. monthly rate = (1.055 -1)/12 = 0.055/12 ≈ 0.0045833 = 0.45833%

  quarterly rate = (1.055 -1)/4 = 0.055/4 = 0.01375 = 1.375%

the answer is b.)

< 1=< 2