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

Answer:

5 I took the test and got this one right.

Answer 2

Answer:

5

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:

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