The bar graph shows your chances of surviving to various ages once you reach 60. Chances of 60-Year-Olds Surviving to Various Ages 90% 86 75% 45% 30% 24 ô 60% 60 15% 2.7 70 80 90 100 Age Source: National Center for Health Statistics The functions f(x)=-2.9x+286 and g(x)=0.01x^2-4.9x+370 model the chance, as a percent, that a 60-year-old will survive to age x. Use this information to solve Exercises 101-102. 101. a. Find and interpret f(70) b. Find and interpret g(70) c. Which function serves as a better model for the chance of surviving to age 70? 102. a. Find and-interpret f(90) b. Find and interpret g(90) c. Which function serves as a better model for the chance of surviving to age 90?

To solve the exercises, we need to evaluate the functions \( f(x) \) and \( g(x) \) at specific ages and interpret the results.<br /><br />### Exercise 101<br /><br />#### a. Find and interpret \( f(70) \)<br /><br />The function is given by \( f(x) = -2.9x + 286 \).<br /><br />\[ f(70) = -2.9(70) + 286 = -203 + 286 = 83 \]<br /><br />**Interpretation:** According to the function \( f(x) \), there is an 83% chance that a 60-year-old will survive to age 70.<br /><br />#### b. Find and interpret \( g(70) \)<br /><br />The function is given by \( g(x) = 0.01x^2 - 4.9x + 370 \).<br /><br />\[ g(70) = 0.01(70)^2 - 4.9(70) + 370 \]<br />\[ = 0.01(4900) - 343 + 370 \]<br />\[ = 49 - 343 + 370 = 76 \]<br /><br />**Interpretation:** According to the function \( g(x) \), there is a 76% chance that a 60-year-old will survive to age 70.<br /><br />#### c. Which function serves as a better model for the chance of surviving to age 70?<br /><br />Based on the bar graph information provided, compare the calculated values with the actual data. If the bar graph shows a percentage closer to 83%, then \( f(x) \) is a better model; if it is closer to 76%, then \( g(x) \) is a better model.<br /><br />### Exercise 102<br /><br />#### a. Find and interpret \( f(90) \)<br /><br />\[ f(90) = -2.9(90) + 286 = -261 + 286 = 25 \]<br /><br />**Interpretation:** According to the function \( f(x) \), there is a 25% chance that a 60-year-old will survive to age 90.<br /><br />#### b. Find and interpret \( g(90) \)<br /><br />\[ g(90) = 0.01(90)^2 - 4.9(90) + 370 \]<br />\[ = 0.01(8100) - 441 + 370 \]<br />\[ = 81 - 441 + 370 = 10 \]<br /><br />**Interpretation:** According to the function \( g(x) \), there is a 10% chance that a 60-year-old will survive to age 90.<br /><br />#### c. Which function serves as a better model for the chance of surviving to age 90?<br /><br />Compare the calculated values with the actual data from the bar graph. If the bar graph shows a percentage closer to 25%, then \( f(x) \) is a better model; if it is closer to 10%, then \( g(x) \) is a better model.<br /><br />By comparing these calculations with the bar graph data, you can determine which function more accurately models the survival chances at each specified age.