http://www.ck12.org Chapter 6. Transcendental Functions
P= 1 + 44994500 e− 0. 8 x
= 1 + 44994500 e− 0. 8 ( 7 )
= 1 + 44994500 ( 0. 004 )
= 255.According to the model, 255 students will become infected with the flu virus. Assume further that the researcher
wants to know how long it will take until 1000 students become infected with the flu virus. Solving forx,
P= 1 + 44994500 e− 0. 8 x.Cross-multiplying,
P( 1 + 4499 e−^0.^8 x)= 4500
1 + 4499 e−^0.^8 x=^4500 P
4499 e−^0.^8 x=^4500 P − 1
=^4500 P−P
e−^0.^8 x=^45004499 −PP.Projecting ln on both sides,
− 0. 8 x=ln[ 4500 −P
4499 P
]
x=ln[ 4500 −P
4499 P
]
÷(− 0. 8 ).
Substituting forP=1000,
x=9 days.So the flu virus will spread to 1000 students in 9 days.
Other applications are introduced in the exercises.
Multimedia Links
For a video presentation of exponential growth involving bacteria (some calculus in part c)(14.0), see Khan Aca
demy, Exponential Growth and Decay (16:00).