Answer: y=x^8-x^7+x^6-x^5+x^4+x^3+x^2+3
Step-by-step explanation:
here is an example function that satisfies the requirement:
y=x^8-x^7+x^6-x^5+x^4+x^3+x^2+3
if you plug in x=0,
you get y= 3, which satisfies (0,3)
if you plug in x=1,
you get y = 1 - 1 + 1 - 1 + 1 + 1 + 1 + 3,
you get y=6, which satisfies (1,6)
The required exponential function which passes through the points (0, 3) and (1, 6) is y = 3[tex]e^{log_{e}2x}[/tex]
Exponential Function:
It is always positive real valued function. The most common and famous exponential function is e^x where e is called base and x is exponent.
Let the required exponential function is y = A[tex]e^{kx}[/tex]
Now we have to find constant A and k with the help of given conditions.
Since this exponential function is passes through the point (0, 3)
Therefore
3 = A e^0
A = 3
Also the exponential function is passes through the point (1, 6)
Therefore
6 = A[tex]e^{k.1}[/tex]
Putting the value of A = 3
3[tex]e^{k\\}[/tex] = 6
[tex]e^k=2\\\\k=log_{e}2[/tex]
Now putting these values in our exponential function equation we have
y = 3[tex]e^{log_{e}2x}[/tex]
This is the required exponential function.
Learn more about Exponential Function here-
https://brainly.com/question/11464095
#SPJ2
