Question

Elementary Functions Me Homework: Week 3 HW Score: 0 of 1 pt 5.5.79 12 of 29 (23 complete) Flowers tend to open in the daylight and close in the dark The percent P of flowers open during a 24-hour period can be modeled by P/x) = sin(x) + d where x is hours past 6 AM (a) Suppose that for P the maximum is 20%, the minimum is 10%, and the period is 24 hours. Determine P[x) (b) When are the most flowers open? (c) When are the fewest flowers open? (a) Determine P(x) P(x)= (Simplify your answer type an exact answer using as needed. Use integers or fractions for any numbers in the expression) Enter your answer in the answer box and then click Check Answer 2 parts 2 remaining Type here to search e

Answer 1

(a) Percentage of flowers opened is modeled by the equation  .

PI) = a.sin(br) +d

Now,we know that maximum value of
sin(br) = 1
,and the minimum value $=-1$ .

So,maximum value of
PI) = a.l+d=a+d
,and minimum value of
PI) = a.1 - d=a-d
.

Then,according the information given in the question,

a + d = 20

a-d= 10

Now,solving these two equation we get,
a = 15
,and $d=5$

Now,we have to use one more information to get the value of .

We know that period of the function
sin(I) = 27
,hence period of the function
sin(6x) =

So,here we have
2п = 24
,i.e.$b=\frac{\pi}{12}$

So,
P(x) = 15sin »*) + 5 = 15sin(19x) + 5
,using
༧ = s

(b) Now,most flowers are open when
7
i,e. when $x=6$ .(because maximum value of
sin (1)
is achieved at $x=\frac{\pi}{2}$ )

So,most flowers are open at 6 hours before 6 A.M i.e. 12 o'clock at midnight.

(c) Fewest flowers are open when $\frac{\pi}{12}x=\frac{3\pi}{2}$ ,i.e when
x = 18
.(because minimum value of
sin (1)
is achieved at
=
).

So,fewest flowers are open at 18 hours before 6 A.M. i.e 12 o'clock at noon.