Question

The function f(x) = 2·5x can be used to represent the curve through the points (1, 10), (2, 50), and (3, 250). What is the multiplicative rate of change of the function?

Answer 1

5 I took the test and got this one right.

Answer 2

5

Step-by-step explanation:

The function is
`f(x) = 2 \cdot 5^(x)`, which means that an increase of a unit in x leads to a multiplicative rate of change of 5 in y. For instance:

`f(1) = 2\cdot 5^(1)`

`f(1) = 10`

`f(2) = 2 \cdot 5^(2)`

`f(2) = 2 \cdot 5\cdot 5`

`f(2) = 50`

`f(2) = f(1) \cdot 5`

`f(3) = 2\cdot 5^(3)`

`f(3) = 2 \cdot 5\cdot 5 \cdot 5`

`f(3) = f(2) \cdot 5`

Therefore, it is proven that:

`f(n) = 5 \cdot f(n-1)`