Thread: log question help

so the equation is
house price = A(2.7)^kt
t= time in years
A and k are constants
price is 112486 when t=3
price is 131593 when t=7

question is to work out A and k

I've been working on it for atleast an hour and i'm stumped
help would be greately appreciated

Originally Posted by immunofort

so the equation is
house price = A(2.7)^kt
t= time in years
A and k are constants
price is 112486 when t=3
price is 131593 when t=7

question is to work out A and k

I've been working on it for atleast an hour and i'm stumped
help would be greately appreciated

No idea how you do it Anyway this is what I tried xD

Note: THIS IS WRONG! so don't read it if you get easily confused

1st Try

112486 = a (2.7)^3k
112486 = 3ak log 2.7
112486 / 3k log 2.7 = a

Replace a in your original equation

112486 = (112468 / 3k log 2.7) 2.7^3k
112486 = (112468 / 3k log 2.7) 3k log 2.7
112486 = 112486

So obviously replacing a was the wrong thing to do, so let's try replacing k.

2nd Try

112486 = a (2.7)^3k
112486 = 3ak log 2.7
112486 / 3a log 2.7 = k

Replace k in your original equation

112486 = a (2.7)^3(112486 / 3a log 2.7)
112486 = a 3(112486 / 3a log 2.7) log (2.7)
112486 = 3a log 2.7 (112486 / 3a log 2.7)
112486 = (3a log 2.7 112486) / ((3a log 2.7)^2)
112486 = 112486 / 3a log 2.7
112486^2 = 3a log 2.7
112486^2 / 3log 2.7 = a

Now let's find k

112486 / 3a log 2.7 = k
112486 / (3 (112486^2 / 3 log 2.7) log 2.7) = k
112486 / (3 (112486^2 /3) = k
112486 / 112486 = k
1 = k

Now let's see if it works out... So replace everything in your original equation.

112486 = a (2.7)^3k
112486 = (112486^2 / 3log 2.7) (2.7) ^ 3*1
112486 = 19.683 (112486^2 / 3log 2.7)
112486 = 19.683 * 1819362976
= Wrong xD

I'm thinking maybe i missed out something when i described the problem, I have uploaded a image of the text


oh and even better if you can help me out with question 5