Answer:
10.5 minutes
Step-by-step explanation:
Thinking about the problem
The modeling function is of the form P(t)=A⋅Bf(t), where B=4B=4B, equals, 4 and f(t)=\dfrac{t}{10.5}f(t)=
10.5
t
f, left parenthesis, t, right parenthesis, equals, start fraction, t, divided by, 10, point, 5, end fraction.
Note that each time f(t)f(t)f, left parenthesis, t, right parenthesis increases by 111, the quantity is multiplied by B=4B=4B, equals, 4.
Therefore, we need to find the ttt-interval over which f(t)f(t)f, left parenthesis, t, right parenthesis increases by 111.
Hint #22 / 3
Finding the appropriate unit interval
fff is a linear function whose slope is \dfrac{1}{10.5}
10.5
1
start fraction, 1, divided by, 10, point, 5, end fraction.
This means that whenever ttt increases by \Delta tΔtdelta, t, f(t)f(t)f, left parenthesis, t, right parenthesis increases by \dfrac{\Delta t}{10.5}
10.5
Δt
start fraction, delta, t, divided by, 10, point, 5, end fraction.
Therefore, for f(t)f(t)f, left parenthesis, t, right parenthesis to increase by 111, we need \Delta t=10.5Δt=10.5delta, t, equals, 10, point, 5. In other words, the ttt-interval we are looking for is 10.510.510, point, 5 minutes.
Hint #33 / 3
Summary
The number of people who yawned quadruples every 10.510.510, point, 5 minutes.
and use algebra to prove the statement.
. Multiply this by ten to get 
. Subtract the initial equation to give 
and divide by 
to see that 
. Substituting into the original equation gives