Question

The table on the left is that of a linear function, and the one on the right is that of an exponential function.

Can you tell which function has the higher rate of growth? How?


A) There is not enough information to make a conclusion.


B) The linear function is growing faster, because at x = 3 the y-value of the linear function is larger.


C) The exponential function is growing faster, because at x = 0 the y-value of the exponential function is larger.


D) The exponential function is growing faster, because it grows by a factor that is multiplied by the previous y-value instead of being added like the linear function.

Answer 1

The exponential function is D. The exponential function is growing faster, because it grows by a factor that is multiplied by the previous y-value instead of being added like the linear function.

What is an exponential function

An exponential function is a mathematical function written as
`( f(x) = a \cdot b^x \)`, where a represents the initial value, b is the constant base
`( > 0), and \( x \)` is the variable exponent.

Their graphs display distinct curves, illustrating steep increase or decrease, and they find applications in finance, population growth, radioactive decay, and other scientific and economic phenomena.

The linear function grows by a * b

exponential grows by aˣ

Option D is correct

Answer 2

The answer is option D) The exponential function is growing faster, because it grows by a factor that is multiplied by the previous y-value instead of being added like the linear function.

Explanation:

Based on the table of the question, we can represent the grapsha by the following equations

Linear

f(x) = 7*x

Exponential

f(x) = 2^x

Which are consistent with the table values.

Exponential functions grow faster than linear functions.

We can easily that by evaluating both functions at x = 10

Linear

f(x) = 7*10 = 70

Exponential

f(x) = 2^(10) = 1024

Note the difference between both. Imagine for numbers greater than 10.