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The number of deaths in a year attributed to AIDS is indicated in Table $10 .$ Using the years 1981 through 1993 find the best fit (a) exponential (b) power function representing this data. (Let 1981 be year 1,1982 year $2,$ and so on.) (c) (i)Find another best fit exponential and (ii) power function that represents the data from years 1993 through 1997 . What reasons can you give to explain the different number of deaths in the late 1980 s and early 1990 s as compared with the later 1990 s and early 2000 s? Source: Centers for Disease Control and Prevention: HIV/AIDS Surveillance Report;1 5$$\begin{array}{|cc||cl||cl|}\hline \text { Year } & \text { Deaths } & \text { Year } & \text { Deaths } & \text { Year } & \text { Deaths } \\\hline \hline 1981 & 130 & 1988 & 21244 & 1995 & 51414 \\1982 & 466 & 1989 & 28054 & 1996 & 38074 \\1983 & 1511 & 1990 & 31836 & 1997 & 21846 \\1984 & 3526 & 1991 & 37106 & 1998^{*} & 19005 \\1985 & 6996 & 1992 & 41849 & 1999^{*} & 18491 \\1986 & 12183 & 1993 & 45733 & 2000^{*} & 17741 \\1987 & 16488 & 1994 & 50657 & 2001^{*} & 18524 \\\hline\end{array}$$

(a) $366.071(1.5555)^{x}$(b) $119.983 x^{2.4257}$(c) (i) $67438.537(0.8384)^{x}$ (ii) $55732.2088 x^{-0.3533} ;$ better information, better treatment, contraception, among other reasons.

Algebra

Chapter 4

Exponential and Logarithmic Functions

Section 2

Exponential Functions

Harvey Mudd College

Baylor University

Lectures

02:58

During the early years of …

01:14

01:15

Death Rate from AIDS. The …

we have given f off X as 3200 X minus 1982 full square plus 1586 and g off X is equal toe 1900 multiplied by X minus 1982 World Square plus 619 and in first part we have been asked to broader Grab off at X is equal toe G off X divided by left off X. When we drew the grab, we get this up in the window 1982 to 1994 by 0 to 1. This is the grap. Disagree up. Intercept this get up interprets their issue off the debts. Do that kisses Oh card In that year In second part, we have to compute the race. So for each year it means in 1982 the rest will be equal to 619. Divide by 1586 and this will be equal toe Jiro 0.39 in 1984 The ritual big toe 1 5600 05 divided by 10,090 927 and this is equal to 0.51 in 1986 that is always equal to 24,593 divided by for 191 deer. And this is equal to 0.586 in 1988. The ratio is equal toe 61 woman 911 divide by one leg. 6304 and this is equal to 0.58 So in 1990 the ratio is equal toe 1 28 level underwear by 1 96 576 and this is equal to 0.61 for in 1992 the ratio is equal to 196 to 83 divided by 32 9 to 05 and the race is equality 0.5 96 In 1994 the issue is equal toe toe, 75 33 divided by 44108 and the ratio is equal to 0.61 toe Did are the ratio's off the That's by cases from 1982 to 1984

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