Question

The expression

475


⋅


1.07


6


t


475⋅1.076


t


475, dot, 1, point, 076, start superscript, t, end superscript models the average annual per capita health care costs, in dollars, in the US as a function of the number of years since


1970


19701970.


What does


1.076


1.0761, point, 076 represent in this expression?

Answer 1

Rate of annual increase

Explanation:

Given that the expression
`475\cdot1.076^t,` models the average annual per capita health care costs, in dollars, in the US as a function of the number of years t since 1970 .

1.076 in the expression
`475\cdot1.076^t,` represents the rate of annual increase of the annual per capita health care costs (in dollars).

Take for example,

In Year 1, when t=1,
`475\cdot1.076^(1)`

In Year 2, when t=2,
`475\cdot1.076^(2)=475\cdot1.076\cdot1.076=(Year 1)\cdot1.076`

Once we know the annual per capita health care costs for the previous year, we simply multiply it by 1.076 or for any number of years, raise it to t years.