Both of these functions grow as x gets larger and larger. Which function eventually exceeds the other?
g(x)=6^x+7
f(x)=6.5x^2+11
To determine which function eventually exceeds the other for larger values of x, we can compare their growth rates.
As x gets larger, the exponential function g(x) = 6^x will grow faster, as exponential growth outpaces quadratic growth. Despite the constants added in both functions (7 in g(x) and 11 in f(x)), the exponential growth in g(x) will eventually cause it to exceed the quadratic growth in f(x).
Therefore, the function g(x) = 6^x + 7 will eventually exceed the function f(x) = 6.5x^2 + 11 for larger values of x.