Question

ASAP! The graph of an exponential model in the form y = a ⋅ bx passes through the points (1, 10) and (2, 20). Which point is also located on the graph? a) (0,0) b) (0,5) c) (3,30) d) (2,20)

Answer 1

Answer:

b

Step-by-step explanation:

Because y increases by a factor of 2 every time x goes up by 1, the opposite happens when x decreases by 1. This means that when x = 0, y = 5 so the answer is b.

Answer 2

Applying the points and finding the equation, it is found that point (0,5) is also on the graph, option b.

The exponential equation has the following format:

$y = ab^x$

Point (1,10) means that when $x = 1, y = 10$, thus:

$ab = 10$

Point (2,20) means that when $x = 2, y = 20$, thus:

$ab^2 = 20$

From the first equation:

$a = \frac{10}{b}$

Replacing on the second:

$\frac{10}{b}b^2 = 20$

$10b = 20$

$b = \frac{20}{10}$

$b = 2$

So

$a = \frac{10}{b} = \frac{10}{2} = 5$

Then, the equation is:

$y = 5(2)^x$

When $x = 0, y = 5(2)^0 = 5$, thus point (0,5) is also on the graph, which means that option b is correct.

A similar problem is given at https://brainly.com/question/14773454