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?
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.