Question

Writing Linear and Exponential EquationsAn investment is initially worth $10,500. Write an equation representing the value of this investment V after t years ineach of the following situations.V=a) The value increases by 9% per yearV=b) The value decreases by $788 per yearV=c) The value decreases by 8% per yearVd) The value increases by $640 per yearNuestion Heln: Post to forum

Answer 1

A.

`V=10500\cdot1.09^t`

B.

`V=10500-788t`

C.

`V=10500\cdot0.92^t`

D.

`V=10500+640t`

Explanation:

We must bear in mind that when a value increases or decreases in percentage form, the form of the equation is exponential, while when it increases or decreases in a fixed manner, the form of the equation is linear.

Starting from the equation, the equations would then be:

A.

`\begin{gathered} V=10500\cdot(1+9\%)^t \\ V=10500\cdot(1+0.09)^t \\ V=10500\cdot1.09^t \end{gathered}`

B.

`V=10500-788t`

C.

`\begin{gathered} V=10500\cdot(1-8\%)^t \\ V=10500\cdot(1-0.08)^t \\ V=10500\cdot0.92^t \end{gathered}`

D.

`V=10500+640t`