Question

A person gives away 1 penny on day zero, 2 pennies on the 1st day, 4 pennies on the 2nd day, 8 pennies on the 3rd day, 16 pennies on the 4th day, and so on.
1) Is this a linear or an exponential function?

2) Write a function f(x) for the number of pennies given on day x.

Answer 1

A function can represent a linear relationship or a non-linear relationship

• The function is an exponential function
• The function for the number of pennies given as: f(x) = 2^x

How to determine the function type

From the question, we have that:

The pennies given each day is 2 multiplied by the penny given on the previous day.

Since the function involves products, then it is an exponential function

The function equation

The initial value of the function is:

a = 1

The rate of the function is given as:

r = 2

An exponential function is represented as:

$f(x) = ar^x$

So, we have:

$f(x) = 1 * 2^x$

$f(x) = 2^x$

Hence, the function for the number of pennies given as: f(x) = 2^x

Read more about exponential functions at:

https://brainly.com/question/11464095