x%09f(x)=a⋅bx%0D%0Ax0%09a⋅bx0%0D%0Ax0+Δx%09a⋅b(x0+Δx)%0D%0Ax0+2Δx%09a⋅b(x0+2Δx)%0D%0ARamona wants to use the table to prove something about how exponential functions grow. What does she need to do next and what will she be able to prove?

Answer 1

To prove something about how exponential functions grow using the given table, Ramona needs to observe the relationship between x, f(x), and a⋅bx.

Next, Ramona can calculate the ratio between the consecutive values of f(x) and a⋅bx. In other words, she needs to divide each f(x) value by the corresponding a⋅bx value.

If Ramona finds that the ratio is approximately constant for all pairs of consecutive values, then she will be able to prove that the function a⋅bx grows exponentially. The constant ratio would indicate that the value of a⋅bx is increasing by the same factor at each step, confirming the exponential growth pattern.