Question: Consider the rational function model f(t)=A t+B f ( t ) = A t + B for real constantsA A andB B . This template
Consider the rational function model
f(t)=A
t+B
f
(
t
)
=
A
t
+
B
for real constantsA
A
andB
B
. This template can be used to model phenomena whose value decreases toward a constant ast
t
increases.(a) Ast
t
increases without bound,f(t)
f
(
t
)
will approach. (Your answer may contain unknown constants)
(b) The vertical axis intercept of the graph off
f
is: (,) (Your answer may contain unknown constants)
(c) While driving, Mychal accidentally runs over a nail and it punctures one of his tires. While waiting for help, he models the tire pressure over time. Initially the pressure is 35 psi (pounds per square inch) and when he checks after 3 minutes, the pressure is 29 psi. Find the values of constantsA
A
andB
B
that model tire pressure over time.
A=.
B=.
(d) Using Mychal's function model in part (c), determine the time at which the tire reaches the atmospheric pressure of about 14.74 psi.
t=
t
=
.
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