The <u>general</u> <u>expression</u> for the <u>exponential function</u> is
where ![a\neq 0,\ b>0,\ b\neq 1.](https://tex.z-dn.net/?f=a%5Cneq%200%2C%5C%20b%3E0%2C%5C%20b%5Cneq%201.)
Note that the graph of each exponential function passes through the point (0,a), because
Since
then options A and C are false.
First point in options B and D is (0,1), then
![f(0)=1\Rightarrow a=1](https://tex.z-dn.net/?f=f%280%29%3D1%5CRightarrow%20a%3D1)
and you get the expression
for the exponential function.
Points (0,1), (1,3), (2,9) and (3,27) represent the powers of 3. In this case ![f(x)=3^x.](https://tex.z-dn.net/?f=f%28x%29%3D3%5Ex.)
Points (0,1), (1,2), (2,5) and (3,10) couldn't generate any exponential function, because if
then ![b^2=2^2=4\neq 5.](https://tex.z-dn.net/?f=b%5E2%3D2%5E2%3D4%5Cneq%205.)
Answer: correct choice is D