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

The Correct Answer would be C 

Answer 2

Answer-

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

Solution-

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

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

The general form of exponential function for growth is,

$f(x)=a(1+r)^x$

where

a = initial value

r = rate of growth

Comparing this with the given function,

a = initial number of members = 10

r = rate of growth = 30% = 0.3

As number of people as well as years can not be negative, so the graph will only be in the quadrant 1.

As it represents the growth so it will start from the left and will move in right direction.

As there are 10 people at the beginning, so the starting point of the graph will be (0, 10) not the origin.

So, option C "Graph of f of x equals 10 multiplied by 1.3 to the power of x" is the correct description of the function.