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?

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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?

Answer 1

To solve the exercises, we need to evaluate the functions \( f(x) \) and \( g(x) \) at specific ages and interpret the results.### Exercise 101#### a. Find and interpret \( f(70) \)The function is given by \( f(x) = -2.9x + 286 \).

**Interpretation:** According to the function \( f(x) \), there is an 83% chance that a 60-year-old will survive to age 70.#### b. Find and interpret \( g(70) \)The function is given by \( g(x) = 0.01x^2 - 4.9x + 370 \).

**Interpretation:** According to the function \( g(x) \), there is a 76% chance that a 60-year-old will survive to age 70.#### c. Which function serves as a better model for the chance of surviving to age 70?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.### Exercise 102#### a. Find and interpret \( f(90) \)

**Interpretation:** According to the function \( f(x) \), there is a 25% chance that a 60-year-old will survive to age 90.#### b. Find and interpret \( g(90) \)

**Interpretation:** According to the function \( g(x) \), there is a 10% chance that a 60-year-old will survive to age 90.#### c. Which function serves as a better model for the chance of surviving to age 90?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.By comparing these calculations with the bar graph data, you can determine which function more accurately models the survival chances at each specified age.

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