Question

In 3-4 sentences, answer this question:
Consider the following two functions: f(x)= 3x+10 and g(x)=5(1.5)^x and answer the following in complete sentences. Which equation is exponential and which is linear? What feature of each equation lets you know that the function is exponential or linear?

Answer 1

The function \( f(x) = 3x + 10 \) is linear because it can be expressed in the form \( y = mx + b \), where \( m \) and \( b \) are constants. In contrast, the function \( g(x) = 5(1.5)^x \) is exponential, as it involves a variable \( x \) in the exponent, indicating that the output grows by a constant percentage. The key feature that distinguishes the two is that linear functions change by fixed amounts, while exponential functions increase or decrease by fixed ratios.