Question

The table below shows the values of f(x) and g(x) for different values of x. One of the functions is a quadratic function, and the other is an exponential function. Which function is most likely increasing exponentially?

Answer 1

$f(x)=x^2+1\\\\for\ x=1\to f(1)=1^2+1=1+1=2\\for\ x=2\to f(2)=2^2+1=4+1=5\\for\ x=3\to f(3)=3^2+1=9+1=10\\for\ x=4\to f(4)=4^2+1=16+1=17\\for\ x=5\to f(5)=5^2+1=25+1=26\\\\g(x)=2^x\\\\for\ x=2\to g(1)=2^1=2\\for\ x=2\to g(2)=2^2=4\\for\ x=3\to g(3)=2^3=8\\for\ x=4\to g(4)=2^4=16\\for\ x=5\to g(5)=2^5=32$

$g(x)\ is\ an\ exponential\ function.$