Answer:
[tex]\dfrac{0.7\pi}{5.3}\cos(\dfrac{2\pi t}{5.3})[/tex]
0.16
Step-by-step explanation:
According to the question the mathematical model should be
[tex]B(t)=2.9+0.35\sin(\dfrac{2\pi t}{5.3})[/tex]
Differentiating with respect to time we get
[tex]B'(t)=0.35\cos(\dfrac{2\pi t}{5.3})\times(\dfrac{2\pi}{5.3})\\\Rightarrow B'(t)=\dfrac{0.7\pi}{5.3}\cos(\dfrac{2\pi t}{5.3})[/tex]
So, the rate of change of brightness after t days is [tex]\dfrac{0.7\pi}{5.3}\cos(\dfrac{2\pi t}{5.3})[/tex]
After 1 day means [tex]t=1[/tex]
[tex]B'(1)=\dfrac{0.7\pi}{5.3}\cos(\dfrac{2\pi\times 1}{5.3})\\\Rightarrow B'(1)=0.16[/tex]
The rate of increase after one day is 0.16.
