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

Graph of f(x)=10(1.3)^x

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

Answer 2

The correct option is 3. Graph of f of x equals 10 multiplied by 1.3 to the power of x.

Explanation:

The number of members f(x) in a local swimming club increased by 30% every year over a period of x years.

The given function is

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

This function interpreted as the function f of x equals 10 multiplied by 1.3 to the power of x. So, the graph of f of x equals 10 multiplied by 1.3 to the power of x.

Therefore the correct option is 3.

Substitute x=0 in the given function.

`f(x)=10(1.3)^0=10`

The function passes through (0,10).

Therefore, option 2 is incorrect.