I really don’t know I’m just here to get points but pennies is the answer sorry
You have a function
![y= \dfrac{3}{2} \left(1+\sin \left(\dfrac{2t+1}{2}\cdot \pi\right) \right)](https://tex.z-dn.net/?f=y%3D%20%5Cdfrac%7B3%7D%7B2%7D%20%5Cleft%281%2B%5Csin%20%20%5Cleft%28%5Cdfrac%7B2t%2B1%7D%7B2%7D%5Ccdot%20%5Cpi%5Cright%29%20%5Cright%29)
.
Since the range of the function
![y=\sin x](https://tex.z-dn.net/?f=y%3D%5Csin%20x)
is
![[-1,1]](https://tex.z-dn.net/?f=%5B-1%2C1%5D)
you have that
![-1\le \sin \left(\dfrac{2t+1}{2}\cdot \pi\right)\le 1 \\ 0\le 1+\sin \left(\dfrac{2t+1}{2}\cdot \pi\right) \le 2 \\ 0\le \dfrac{3}{2} \left(1+\sin \left(\dfrac{2t+1}{2}\cdot \pi\right) \right)\le 3](https://tex.z-dn.net/?f=-1%5Cle%20%5Csin%20%5Cleft%28%5Cdfrac%7B2t%2B1%7D%7B2%7D%5Ccdot%20%5Cpi%5Cright%29%5Cle%201%20%5C%5C%200%5Cle%201%2B%5Csin%20%5Cleft%28%5Cdfrac%7B2t%2B1%7D%7B2%7D%5Ccdot%20%5Cpi%5Cright%29%20%5Cle%202%20%5C%5C%200%5Cle%20%5Cdfrac%7B3%7D%7B2%7D%20%5Cleft%281%2B%5Csin%20%5Cleft%28%5Cdfrac%7B2t%2B1%7D%7B2%7D%5Ccdot%20%5Cpi%5Cright%29%20%5Cright%29%5Cle%203)
.
Answer: The range of given function is [0,3] and the correct choice is C.
Answer: 0.648637
Explanation:
e^3x = 3 + 4
e^3x = 7
3x = In (7)
X = 0.648637