c=2.85n +30.52 where n is the namber of years since1990. a)find and interpret the C-intercept for the line,b)find and interpret the n-intercept for the line,C) graph the line for n ranging from 0 through 20,d)if this trend continues,then in what year will the cost of dental service reach 100billion?
a) To find the C-intercept of the line, we need to substitute n = 0 into the equation and solve for C. Let's do that:
c = 2.85n + 30.52
Substitute n = 0:
c = 2.85(0) + 30.52
c = 0 + 30.52
c = 30.52
So, the C-intercept is 30.52. Interpreting this value, it means that in the year 1990 (when n = 0), the cost (c) of dental services is estimated to be $30.52 billion.
b) To find the n-intercept of the line, we need to substitute c = 0 into the equation and solve for n. Let's do that:
0 = 2.85n + 30.52
Subtract 30.52 from both sides:
-30.52 = 2.85n
Divide both sides by 2.85:
n = -30.52 / 2.85
n ≈ -10.70
So, the n-intercept is approximately -10.70. However, since n represents the number of years, we round it up to 11. Interpreting this value, it means that around the year 1979 (1990 - 11), the cost of dental services was estimated to be zero.
c) To graph the line, we need to plot a graph with n on the x-axis and c on the y-axis. The range of n is given as 0 through 20.
Plot the points (0, 30.52) and (20, c), where c is calculated as follows:
c = 2.85(20) + 30.52
c = 57 + 30.52
c = 87.52
Plot the point (20, 87.52). Now connect the two points with a straight line. This line represents the relationship between n and c.
d) To determine in what year the cost of dental service will reach $100 billion, we need to set up the equation and solve for n:
100 = 2.85n + 30.52
Subtract 30.52 from both sides:
69.48 = 2.85n
Divide both sides by 2.85:
n = 69.48 / 2.85
n ≈ 24.35
Since n represents the number of years since 1990, rounding up to the nearest whole number, the cost of dental services will reach $100 billion around the year 2015 (1990 + 24).
Note: This answer assumes that the trend given by the equation continues, and it may not account for other factors that could impact the cost of dental services in the future.