The table gives the total emissions of lead into the atmosphere for selected years.Total Lead Emissions into the AtmosphereLead, f(million tons)Year1970220.9159.71975198074.222.9198519905.019953.9(a) Find a logistic function that models the data. (Align the input data so that t 0 in 1970. Round all numerical values to three decimal places.)f(t)(b) Estimate the location of the inflection point. (Round your answer to the nearest integer.)t =(c) Indicate where the curve is concave up and where it is concave down.OThe curve is concave down when t is less than the inflection point and is concave up when t is greater than the inflection point.OThe curve is concave up when t is less than the inflection point and is concave down when t is greater than the inflection point.

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Asked Aug 30, 2019
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The table gives the total emissions of lead into the atmosphere for selected years.
Total Lead Emissions into the Atmosphere
Lead, f
(million tons)
Year
1970
220.9
159.7
1975
1980
74.2
22.9
1985
1990
5.0
1995
3.9
(a) Find a logistic function that models the data. (Align the input data so that t 0 in 1970. Round all numerical values to three decimal places.)
f(t)
(b) Estimate the location of the inflection point. (Round your answer to the nearest integer.)
t =
(c) Indicate where the curve is concave up and where it is concave down.
OThe curve is concave down when t is less than the inflection point and is concave up when t is greater than the inflection point.
OThe curve is concave up when t is less than the inflection point and is concave down when t is greater than the inflection point.
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The table gives the total emissions of lead into the atmosphere for selected years. Total Lead Emissions into the Atmosphere Lead, f (million tons) Year 1970 220.9 159.7 1975 1980 74.2 22.9 1985 1990 5.0 1995 3.9 (a) Find a logistic function that models the data. (Align the input data so that t 0 in 1970. Round all numerical values to three decimal places.) f(t) (b) Estimate the location of the inflection point. (Round your answer to the nearest integer.) t = (c) Indicate where the curve is concave up and where it is concave down. OThe curve is concave down when t is less than the inflection point and is concave up when t is greater than the inflection point. OThe curve is concave up when t is less than the inflection point and is concave down when t is greater than the inflection point.

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Expert Answer

Step 1

(a) Let us align the input data so that t = 0 in 1970.

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Lead, f (million tons) Year 0 220.9 5 159.7 10 72.4 15 22.9 20 25 3.9

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Step 2

The logistic model is shown below:

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Lead, f (million tons) Year 0 220.9 159.7 5 -200 72.4 10 15 22.9 20 5 25 3.9 a 1 b x 10 20 15 STATISTICS RESIDUALS RMSE-0 e plot PARAMETERS 0 b 0.136863 a 0 t 0.288073

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Step 3

(b) Inflation point is where the curvature of the graph changes direction. Here, we can see that at t = 8 the graph changes dire...

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251.311 y = 1 (0.136863) e0.288073x 200 Inflation point (8, 105.977) 100 25 10 -5 15 20

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