A house was valued at 115000 in the year 1994 the value...

Name: a house was valued at 115000 in the year 1994 the value appreciated to 150000 by the year 2006 a what was the annual growth rate between 1994 and 2006 round the growth rate to 4 decimal plac 11986
Uploaded: 2023-07-07T03:17:06-08:00
Duration: 5 min 2 s
Channel: Danielle Fairburn
Description: a house was valued at 115000 in the year 1994 the value appreciated to 150000 by the year 2006 a what was the annual growth rate between 1994 and 2006 round the growth rate to 4 decimal plac 11986

A house was valued at $115,000 in the year 1994. The value appreciated to $150,000 by the year 2006. A) What was the annual growth rate between 1994 and 2006? = Round the growth rate to 4 decimal places.

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Transcript

00:01 So let's set 1992 equal to t is zero and then t will be the number of years since 1992.

00:18 And we're told that the house value was equal to 120 ,000 in the year 1992.

00:28 So our initial amount or initial value was 120 ,000.

00:34 And then the house appreciated to 155 ,000 in 2000.

00:50 Well, 2000 is eight years since 1992.

00:57 So this is the amount when t is equal to eight.

01:03 And then the formula for the amount in year t will be the initial amount times one plus the annual growth rate r to the t, where r is the annual growth rate.

01:23 So we can solve for r by using the values that we have.

01:34 We know that this then is equal to our a0 was 120 ,000 times one plus r to the t.

01:45 And we know that a when t is eight is equal to 155 ,000.

01:55 And according to our formula, that's equal to 120 ,000 times one plus r to the eighth power.

02:04 So dividing both sides by 120 ,000, we get 155 divided by 120.

02:11 Those zeros drop away.

02:13 This then is equal to one plus r to the eighth.

02:17 That means that if we take this to the one eighth and we take that to the one eighth, we get one plus r on the right.

02:27 And that means that r is equal to 155 divided by 120 to the one eighth minus one...

Question

A house was valued at $115,000 in the year 1994. The value appreciated to $150,000 by the year 2006. A) What was the annual growth rate between 1994 and 2006? = Round the growth rate to 4 decimal places.

Please give Ace some feedback