The bar graph shows the percentage of country A high school seniors who applied

Question

The bar graph shows the percentage of country A high school seniors who applied to more Percentage of country A High School Seniors Applying to More Than than three colleges for selected years from 1980 through 2013. The data in the bar graph can be modeled by f(x)-x+26 and g(x) 30.6 e 0.0216x, in which f(x) and g(x) represent the percentage of high school seniors who applied to more than three colleges x years after 1980 Use these functions to complete parts (a) through (c) below. Three Colleges 61 60- 40 32 40 44 48 20 1980 1990 1995 2000 2005 2010 2013 0. Year a. According to the linear model, what percentage of high school seniors applied to more than three colleges in 2005? b. According to the exponential model, what percentage of high school seniors applied to more than three colleges in 2005? % (Round to the nearest percent as needed.) c. Which function is a better model for the data shown by the bar graph in 2005? O A. Linear model OB. Exponential model Click to select your answer(s).

Explanation / Answer

The number of years between 2005 and 1980 equals 25.

So x = 25

We will use x in f(x) and g(x) to get the percentage of high school seniors applied to more than three colleges in 2005.

(a) for linear model we get, f(x) = x + 26

so f(25) = 25 + 26 = 51

(b) for exponential model we get, g(x) = 30.6 * e0.0216x

So g(25) = 30.6 * e0.0216(25) = 52.5

After rounding we get the percentage for exponential model as 53 %

(c) Since the percentage of exponential model is closer to 55% (the percentage in bar graph for year 2005) than linear model we will say that the exponential model is better model.

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