For x = 4, then it means 3 to the fourth power or 3 times 3 times 3 times 3 times 3. 3^4 = 81 and 8 times that is 648.
y(x) = 8 * 3^x where x = 4:
y(x) = 8 * 3^4 = 8 * 81
y(x) = 648
The Function Rule then being that for every value of x there is one and only one value of y. y is the dependent variable and x is the independent variable.
Answer:
![a_n = 3 ({5})^{n - 1}](https://tex.z-dn.net/?f=a_n%20%3D%203%20%28%7B5%7D%29%5E%7Bn%20-%201%7D%20)
Step-by-step explanation:
The given sequence is 3,15,75,375,...
The first term of this geometric sequence is
![a_1=3](https://tex.z-dn.net/?f=a_1%3D3)
The common ratio is
![r = \frac{15}{3} = 5](https://tex.z-dn.net/?f=r%20%3D%20%20%5Cfrac%7B15%7D%7B3%7D%20%20%3D%205)
The explicit formula is given by:
![a_n = a_1 {r}^{n - 1}](https://tex.z-dn.net/?f=a_n%20%3D%20a_1%20%7Br%7D%5E%7Bn%20-%201%7D%20)
We plug the first term and common ratio into the formula to get:
![a_n = 3 ({5})^{n - 1}](https://tex.z-dn.net/?f=a_n%20%3D%203%20%28%7B5%7D%29%5E%7Bn%20-%201%7D%20)
The answer would be 16.
8+8=16