The table shows the populations P (in millions) of the United States from 1960 to 2000. Year 1960 1970 1980 1990 2000 Popupation, P 181 205 228 250 28

sanuluy

sanuluy

Answered question

2021-06-02

The table shows the populations P (in millions) of the United States from 1960 to 2000. Year 1960 1970 1980 1990 2000 Popupation, P 181 205 228 250 282
(a) Use the 1960 and 1970 data to find an exponential model P1 for the data. Let t=0 represent 1960. (c) Use a graphing utility to plot the data and graph models P1 and P2 in the same viewing window. Compare the actual data with the predictions. Which model better fits the data? (d) Estimate when the population will be 320 million.

Answer & Explanation

Nicole Conner

Nicole Conner

Skilled2021-06-03Added 97 answers

(a) We have the equation P=Cekt where t is the number of years since 1960. Setting t= 0, we have 181=Ce0=C. To find the rate k, we can tse the 1970 data: 205=181e10k
k=110(ln(205181))=0.1245
This gives us the model P1=181e0.01245t
(b) Using a graphing utiliti gives us the model P2=182.32e0.0109t
(c) P1 i black, while P2 is graphed in blue:
(d) Setting P2=320, we can then solve for t to get:
t=ln1.75520.010951 years, or in the year 2011.

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