Question

The table shows the value y of a condominium (in thousands of dollars) after x years. Write an

exponential function that models the value y of the condo after x years.
Year, x
Value, y (dollars)
0
150
1
156
2
162.24
3
168.7296

Answer 1

The exponential function that models the value of the condominium after x years is y = 150 *
`1.04^x`, where y represents the value of the condominium in thousands of dollars and x represents the number of years. The initial value is 150, and the growth factor is approximately 1.04.

To write an exponential function that models the value y of the condominium after x years, we can use the general form of an exponential function: y = a *
`b^x`.

Let's analyze the given data:

Year, x Value, y (dollars)

0 150

1 156

2 162.24

3 168.7296

We can see that the value of the condominium is increasing over time, indicating exponential growth.

To determine the values of a and b in our exponential function, we can use the data provided.

From the table, we can observe that when x = 0, y = 150. This gives us the value of a, which is the initial value or the y-intercept. So, a = 150.

Next, we need to find the value of b, which is the growth factor or the base of the exponential function. We can do this by considering the ratio of y values for consecutive years.

From the data, we can see that the value of y increases by a factor of approximately 1.04 each year. This means that b = 1.04.

Therefore, the exponential function that models the value y of the condominium after x years is:

y = 150 *
`1.04^x`

The question probable may be:

The table shows the value y of a condominium (in thousands of dollars) after x years. Write an exponential function that models the value y of the condo after x years.

Year, x Value, y (dollars)

0 150

1 156

2 162.24

3 168.7296