Question

The function LaTeX: f\left(x\right)=2\cdot5^xf ( x ) = 2 ⋅ 5 x can be used to represent an exponential growth curve. Which of the following points is NOT on the curve? (3, 250) (2, 20) (1, 10) (2, 50)

Answer 1

Answer:

(2,20)

Step-by-step explanation:

The given function is

$f(x) = 2 \cdot \: {5}^{x}$

To see which point is not on this curve, we must substitute the points to see which does not satisfy the equation;

For the first point we substitute x=3 and f(x)=250

$250= 2 \cdot \: {5}^{3} \: \\ 250 = 2 \times 125 \\ 250 = 250$

This is true.

For the second point (2,20), we put x=2 and y=20 to get:

$20= 2 \cdot \: {5}^{2} \\ 20 = 2 \times 25 \\ 20 = 50$

This is false, hence (2,20) does not lie on this curve.

For (1,10), we have:

$10= 2 \cdot \: {5}^{1} \\ 10 = 10$

This is also true

Finally for (2,50), we have;

$50= 2 \cdot \: {5}^{2} \\ 50 = 2 \times 25 \\ 50 = 50$

This is also true.