Question

Am I right? Take a quick look?

You purchase a house in 1995 for $95000. The house increases per year you own it.
Write the exponential model for the value of the house.
A= 95000(1.03)^t
Use the model to find the value of the house after 10 years.
A= 127,672.056
How long will it take until the value of the house reaches $50,000?
T= 1.533 years

Answer 1

If the value of the house increases by 3% per year, 1 and 2 look correct.

For the third one, how can the house reach a value of $50,000 if it's alrady worth $95,000? Are you sure they don't actually mean $50,000 value increase?

Answer 2

Dude i wish i knew but thats what the question says. Not much i can do about that but yeah they probably meant that.

Answer 3

Then, how did you get T= 1.533 years?

Answer 4

Thats the equation and got that.answer

Answer 5

\[50000=95000 \times (1.03)^t \]\[\frac{ 50000 }{ 95000} = \times (1.03)^t\]\[\large t = \frac{ \lg(\frac{ 50000 }{ 95000}) }{ \lg(1.03) } \approx -21.71\]

Answer 6

Disregard that multiplication sign on the right side in the middle one

Answer 7

Anyway I think a $50000 will produce a better answer because answers in negative time usually's not correct.

Answer 8

Actually I recalculated it and i got a negative this time so yeah. . .. .

Answer 9

a $50000 value increase*

Answer 10

So would it be like no solution or something.

Answer 11

Yeah, depending on how you interpret the question.
Either that, or if it's a $50000 value incerase then you'll get the equation \[95000+50000= 95000 \times 1.03^t \]

Answer 12

which has a positive soulution

Answer 13

Alright. Thanks.

Answer 14

Yw, no problem :)