Question

Select the scenarios that correctly represent the given graph.

Answer 1

Answers: The correct choices are the first two choice.

The graph shown is an exponential graph. From the first point to the second, it increase from 100 to 150. This is a 50% increase. This pattern continues throughout the chart.

The first two choices give an increase of 50%. Or 1.5 times larger.

Answer 2

The correct options are 1 and 2.

Explanation:

From the given graph it is clear that it is a graph of an exponential function and the graph passes through the points (0,100) and (1,150).

The general form of an exponential function is

`y=ab^x` .... (1)

Where, a is the initial value and b is growth rate.

The initial value is 100 because the y-intercept of the graph is 100.

The graph passes through (1,150). Put y=150, a=100 and x=1 in the above formula to find the value of b.

`150=100b^1`

Divide both the sides by 100.

`1.5=b`

The value of b is 1.5.

Substitute a=100 and b=1.5 in equation (1).

`y=100(1.5)^x`

It means the value is 1.5 times larger in every unit of time.

It can be written as

`y=100(1+0.5)^x`

It means the initial value increased by 50% per unit of time.

So, the required scenarios are

1. The amount of money in a bank account increased by 505 per year.

2. The amount of a substance is one and a half times larger after every minute.

Therefore the correct options are 1 and 2.