The number of asthma sufferers in the world was about 84 mil

The number of asthma sufferers in the world was about 84 million in 1990 and 130 million in 2001. Let N| represent the number of asthma sufferers (in millions) worldwide t| years after 1990. (a) Write N| as a linear function of ft Use exact values in your formula, not decimal approximations. N(t) =| million people help (formulas) (b) Write N| as an exponential function of ft Use exact values in your formula, not decimal approximations. N(t) =| million people help (formulas) (c) How many asthma sufferers are predicted worldwide in the year 2010 with the linear model? million people. (Round to the nearest 0.01 million people.) help (numbers) (d) How many asthma sufferers are predicted worldwide in the year 2010 with the exponential model? million people. (Round to the nearest 0.01 million people.) help (numbers)

Solution

The base year is 1990 i.e. t =0

( 1990, 84 million ) ---> ( 0, 84)

( 2001 , 130 million) ----> ( 11 , 130)

a) Linear function : slope = ( 130 -84)/11 = 4.18

N(t) = m*t +c ; N(t) = 4.18t + 84

b) Exponential function : N(t) = Noe^(kt)

= 84e^(kt)

find k using point ( 11, 130) : 130 = 84e^11k

130/84 = e^11k . Take natural log on both sides:

ln(130/84) = 11k ; k = 0.0397

N(t) = 84e^0.0397t

c) 2010 ; t = 10

N(t) = 4.18*10 + 84 = 125.80 million

d) N(t) = 84e^0.0397t

= 84 e^(0.0397*10) = 84*1.487 = 124.91 million