Question

9. In 2015, 88% of US residents used the internet. The table shows the percent who use the internet for selected years from 2000 and projected to 2025. Year Percent 2000 67 2015 2010 82 79 95 98 (a) Use your calculator to find the natural logarithmic function that models the percent p as a func- tion of x, the number of years after 1990. Report the model with 4 significant digit coefficients. (b) Use the model to predict the percentage of internet users in the United States in 2022.
how?

Answer 1

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ANSWER:

EXPLANATION:

As per question given:

a)

x	p	log x
10	67	2.302585
15	79	2.70805
20	82	2.995732
25	88	3.218876
30	95	3.401197
35	98	3.555348

Using Excel

data -> data analysis -> regression

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.9911
R Square	0.9823
Adjusted R Square	0.9778
Standard Error	1.6941
Observations	6
ANOVA
	df	SS	MS	F	Significance F
Regression	1	635.3535	635.3535	221.3816	0.0001
Residual	4	11.4798	2.8699
Total	5	646.8333
	Coefficients	Standard Error	t Stat	P-value	Lower 95%
Intercept	11.4501	4.9803	2.2991	0.0830	-2.3774
log x	24.2165	1.6276	14.8789	0.0001	19.6976

p^ = 11.4501 + 24.2165 ln x

r = 0.9911

b)

when x = 42

p^ = 11.4501 + 24.2165* ln (42)

= 101.9633

= 102 %

this is not correct because the percentage can't be more than 100

this occurs due to extrapolation error as 2022 is outside sample data

predicting for such value may give error which it does

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