In 1991, the life expectancy of males in a certain company was 68.2 years. In 1997, it was 70.7 years. Let E represent the life expectancy in year t and let t represent the number of years since 1991.
1) The linear function E(t) that fits the date is E(t)=____t+____
Round to the nearest tenth
2) Use the function to predict the life expectancy of males in 2007.
E(16)= ________ round to the nearest tenth.
HELP ME PLEASE !
auren and Andrew left Austin at the same time. Lauren traveled east at an average speed of 50 miles per hour. Andrew traveled west at an average speed of 65 miles per hour. How many hours of driving does it take for the two to be at least 500 miles apart? Write an inequality to model this situation and give the solution rounded to the nearest hundredth. There are directions for how to type math characters in the Resource Center that will show you show to enter your equations.
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To find the linear function that fits the data, we need to determine the slope and the y-intercept of the equation.
The general form of a linear equation is y = mx + b, where m represents the slope and b represents the y-intercept.
1) To find the slope (m), we can use the formula:
m = (y2 - y1) / (x2 - x1)
Using the given data:
x1 = 1991, y1 = 68.2
x2 = 1997, y2 = 70.7
Plugging these values into the formula:
m = (70.7 - 68.2) / (1997 - 1991)
m = 2.5 / 6
m = 0.4167 (rounded to four decimal places)
Now that we have the value of the slope, we can use the point-slope form of a linear equation to find the y-intercept (b).
y - y1 = m(x - x1)
Using x1 = 1991, y1 = 68.2, and m = 0.4167, we get:
y - 68.2 = 0.4167(x - 1991)
Simplifying the equation:
y - 68.2 = 0.4167x - 830.96
Now, let's solve for y:
y = 0.4167x - 762.76
Rounding to the nearest tenth, the linear function E(t) that fits the data is:
E(t) = 0.4t - 762.8
2) To predict the life expectancy in 2007, we need to find the value of E(16), where t represents the number of years since 1991.
Plugging in t = 16 into the equation:
E(16) = 0.4(16) - 762.8
E(16) = 6.4 - 762.8
E(16) = -756.4 (rounded to the nearest tenth)
Therefore, the predicted life expectancy of males in 2007 is approximately -756.4 years (rounded to the nearest tenth). Note that the negative value suggests an error in the calculations or conclusions drawn from the given data.