Question

The number of members f(x) in a local swimming club increased by 30% every year over a period of x years. The function below shows the relationship between f(x) and x:

f(x) = 10(1.3)x

Which of the following graphs best represents the function?

Graph of f of x equals 1.3 multiplied by 10 to the power of x
Graph of exponential function going up from left to right in quadrant 1 through the point 0, 0 and continuing towards infinity
Graph of f of x equals 10 multiplied by 1.3 to the power of x
Graph of f of x equals 1.3 to the power of x

Answer 1

3rd one.

f(x) = 10(1.3)^x

Answer 2

The graphs that best represents the function is:

Graph of f(x) equals 10 multiplied by 1.3 to the power of x.

Explanation:

The function that shows the relationship between f(x) and x: is:

`f(x)=10* (1.3)^x`

a)

Graph of f(x) equals 1.3 multiplied by 10 to the power of x.

This means that the expression is given by:

`f(x)=1.3* (10)^x`

Hence, option: a is incorrect since it is not equal to the given function f(x).

b)

Graph of exponential function going up from left to right in quadrant 1 through the point (0, 0) and continuing towards infinity.

In the given function f(x) when x=0 we have:

`f(x)=10* (1.3)^0\\\\\\f(x)=10\\eq 0`

Hence, option: b is incorrect.

c)

Graph of f(x) equals 10 multiplied by 1.3 to the power of x.

This means that the function f(x) is given by:

`f(x)=10* (1.3)^x`

which is obviously true.

Hence, option: c is correct.

d)

Graph of (x) equals 1.3 to the power of x.

This means that the function f(x) is given by:

`f(x)=(1.3)^x`

which does not m,atches the actual expression.

Hence, option: d is incorrect.