On a remote tropical island, the average life expectancy of women is given by the model
where is the "average life expectancy for a woman" since 1980. Thus, is the number of years since 1980. What is the predicted average life expectancy of a woman in the year 2018?
y=√6000+67x-2.2x^2+.04x^3
Your problem seems to be missing the variables...:(
If you mean
y=√(6000 + 67x - 2.2x^2 + .04x^3)
then since 2018 - 1980 = 38,
y(38) = 86.97
To find the predicted average life expectancy of a woman in the year 2018, we need to substitute the value of x = 2018 into the given equation.
y = √6000 + 67x - 2.2x^2 + 0.04x^3
Let's calculate it step-by-step:
Step 1: Substitute the value of x = 2018 into the equation.
y = √6000 + 67(2018) - 2.2(2018)^2 + 0.04(2018)^3
Step 2: Simplify the equation.
y = √6000 + 135,406 - 8,842.8 + 32,865.52
Step 3: Simplify further.
y ≈ √6000 + 135,406 - 8,842.8 + 32,865.52
y ≈ 77.46 + 135,406 - 8,842.8 + 32,865.52
y ≈ 159,606.72
Therefore, the predicted average life expectancy of a woman in the year 2018 is approximately 159,606.72 years.
To find the predicted average life expectancy of a woman in the year 2018 using the given model, substitute the value of x as the number of years since 1980.
In this case, x = 2018 - 1980 = 38.
Now, plug this value into the equation:
y = √6000 + 67x - 2.2x^2 + .04x^3
y = √6000 + 67(38) - 2.2(38)^2 + .04(38)^3
Calculate each term:
y = √6000 + 2546 - 2.2(38)^2 + .04(38)^3
y = √6000 + 2546 - 2.2(1444) + .04(54872)
y = √6000 + 2546 - 3176.8 + 2194.88
Now, compute the square root of 6000:
y = 77.4598 + 2546 - 3176.8 + 2194.88
Combine like terms:
y = 77.4598 + 2546 - 3176.8 + 2194.88
y = 77.4598 - 3176.8 + 2194.88 + 2546
y = 68.658
Therefore, the predicted average life expectancy of a woman in the year 2018 on the remote tropical island is approximately 68.658 years.