Question

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 t. What is the slope.
b. Write N as a exponential function of t. What is the growth factor
c. How many asthma sufferers are predicted worldwide in the year 2010 with the linear model? With the exponential model?

Answer 1

Answer:

Step-by-step explanation:

Given that 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) If linear function let us assume 1990 as base year 0 then 2001 would be year 11

When written as ordered pairs year and asthma sufferers in millions we have

(0,84) and (11,130) lie on the line

Using two point formula equation of line is

$\frac{y-84}{130-84} =\frac{x-0}{11-0} \\y-84 = \frac{46x}{11} \\y = \frac{46x}{11} +84$

Slope = 46/11

b) When exponential we have

$N =84e^{kt}$

Use N(11) =  $84e^{11k}=130\\k=0.0397$

$N =84e^{0.0397t}$

c) In 2010, t = 20

Linear y(20) = $\frac{46*20}{11} +84\\=167.64$

When exponential

N(20) = $84e^{0.0397*20}\\=185.81$