Question

How do you know if a word problem is talking about exponential functions?

Answer 1

Hint: To solve the given problem, we should know how the exponential functions are written in words as well as in algebraic form. In words, we can write the exponential functions using the phrases like ‘ raised to ‘, ‘ to the power ‘, etc. we will see different examples of exponential functions used in word problems.

Complete step-by-step solution:
Exponential functions are more commonly used for either exponential decay or exponential growth problems. We will see examples of both:
First let’s look at an exponential decay problem. The exponential decay definition states that the quantity in exponential decay decreases very rapidly at the beginning, and then the rate decreases over time. The rate of becoming slower as the time passes. These types of functions are mainly used in activity decay of atoms. The algebraic form for these functions is \[y=a{{(1-r)}^{x}}\].
Now let’s look at exponential growth statements. The exponential definition states that, the quantity in exponential growth increases very rapidly at the beginning, and then the rate increases over time. The rate of becoming faster as the time passes. The algebraic form for these functions is \[y=a{{(1+r)}^{x}}\]. These types of functions can be used for population growth of a certain place.

Note: If the word statement has the words like ‘raised to’, ‘to the power’, or ‘exponentially’. Then the algebraic expression will surely have an exponential term. Exponential functions are used to show growth or decay of a particular entity.