Question

Is each situation a linear or a nonlinear model?

A home’s value is given by the equation y = 154,000(1.04)x, where y is the value of the house and x is the number of years since the home was purchased.

A.


linear model


B.


nonlinear model

Answer 1

it is definitely not a line
a line looks like \(y=mx+b\)

Answer 2

what you have there is an "exponential" model
the variable is in the exponent

Answer 3

@Directrix

Answer 4

Is this >> y = 154,000(1.04)x supposed to be y = 154,000(1.04)^x ?

Answer 5

Yeah sorry :)

Answer 6

It is not linear. If it were, the x would appear as x to the first power.

Answer 7

Okay Thanks :) I only have two more now.

Answer 8

The graph of this: y = 154,000(1.04)^x
is not a line.

Answer 9

Ooh okay

Answer 10

Linear looks like y = 5x + 2.

The big deal is that the x is not raised to a power such as 2 and the x is not an exponent.

Answer 11

You can always graph the function and look and see if the graph is a line.

Answer 12

Oh ok I think my last two might be linear then @Directrix

1.
The amount of money Elijah has in his bank account is given by the equation B = 1400 + 120m, where B is the balance in his account and m is the number of months since he opened the account.
2.
The number of words Sarah can type in a given amount of time is given by the equation w = 32m, where w is the number of words and m is the number of minutes she types.

Answer 13

1 looks like it, and maybe 2?

Answer 14

I agree with you that both are linear.

No exponents, no powers.

Answer 15

Yay thanks so much for teaching how do these :)