Question

Lisa purchases a house for $120,000 in a good area. The value of houses in the area where the house was purchased is averaging an increase of 6% per year. Determine the growth factor and write a function that describes the value of the house t years after it was purchased?

Answer 1

Answer:the growth factor for the value of the house, we need to consider the 6% increase per year.

The growth factor is calculated by adding 1 to the percentage increase in decimal form. In this case, the growth factor is 1 + 0.06, which equals 1.06.

Now let's write a function that describes the value of the house t years after it was purchased. We'll use V(t) to represent the value of the house after t years.

V(t) = initial value * (growth factor)^t

In this case, the initial value is $120,000 and the growth factor is 1.06.

Therefore, the function that describes the value of the house t years after it was purchased is:

V(t) = $120,000 * (1.06)^t

For example, if we want to know the value of the house after 5 years, we can substitute t = 5 into the equation:

V(5) = $120,000 * (1.06)^5

Simplifying the equation gives us the value of the house after 5 years.

Remember, this function assumes that the 6% increase in value remains consistent each year.

Step-by-step explanation: i study it

Answer 2

Growth factor: 1.06

Function:
`\sf V(t) = \$ 120,000 \cdot (1.06)^t`

Explanation:

The growth factor is the percentage increase in value of the house each year. In this case, the growth factor is 6%, which can be expressed as a decimal as follows:

Growth factor = 1 + rate = 1 + 6%= 1 + 0.06 = 1.06

This means that the value of the house increases by 1.06 times each year.

To write a function that describes the value of the house t years after it was purchased, we can use the following formula:

`\sf V(t) = V_0 \cdot (1 + g)^t`

• where:
• V(t) is the value of the house t years after it was purchased
• 
  `V_0` is the initial value of the house
• g is the growth factor

In this case, we have:

• 
  `V_0` = $120,000
• g = 1.06

Therefore, the function that describes the value of the house t years after it was purchased is as follows:

`\sf V(t) = \$ 120,000 \cdot (1.06)^t`