Question

State whether the given sentence is true or false. If false, replace the underlined term to make a true sentence.

An exponential growth equation is$y=C{\left(1-r\right)}^t$

Short answer

The sentence, “The exponential growth equation is $y=C{\left(1-r\right)}^t$. ” is false.

The correct replacement for the underlined term to make a true sentence is exponential decay.

Step-by-step solution

Step 1. Define the meaning of a function.

In mathematics, a function is a rule or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

Step 2. Define an exponential function.

An exponential function is a function that can be described by an equation of the form$y=a{b}^x$ where,$a\ne 0,b>0$ and $b\ne 1$.

Step 3. Check whether the given sentence is true or false.

The equation in the form $y=a{\left(1+r\right)}^t$is a general equation for exponential growth.

The equation in the form $y=a{\left(1+r\right)}^t$is a general equation for exponential decay.

Where,

$y$is the final amount after time $t$.

$a$is the initial amount.

$r$is the rate of change.

Therefore, the sentence, “The exponential growth equation is $y=C{\left(1-r\right)}^t$.” is false.

The correct replacement for the underlined term to make a true sentence is exponential decay.