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 double every 76 years. b the per capita health care costs were about $1,076 in 1970. c the per capita health care costs increase by about 7.6% each year.

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 the costs. Option A refers to doubling time, which is not directly represented by 1.076. Option B is incorrect because 475 is the 1970 cost, not 1076.

Answer:

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