Question

the expression $475 \cdot 1.076^t$ models the average annual per capita health care costs, in dollars, in the us as a function of the number of years since 1970. what does 1.076 represent in this expression? choose 1 answer: a the per capita health care costs increase by about 7.6% each year. b the per capita health care costs double every 76 years. c the per capita health care costs were about $1,076 in 1970.

Explanation:

The given expression follows the exponential growth model $P(t) = P_0(1+r)^t$, where $P_0$ is the initial value, $r$ is the annual growth rate, and $t$ is time. Here, $1.076 = 1 + 0.076$, so $0.076$ (or 7.6%) is the annual growth rate of per capita health care costs. Option B is incorrect because the doubling time is calculated via the rule of 72, not directly tied to 0.076 as 76 years. Option C is incorrect because 475 is the 1970 cost, not 1076.

Answer:

A. The per capita health care costs increase by about 7.6% each year.