# Thread: Find an approimate equation...

1. ## Find an approimate equation...

Find an approximate equation $\displaystyle y=ab^{x}$ of the exponential curve that contains the given pair of points. Round the value of b to two decimal places.

(0, 256) and (7, 23)

my work:

$\displaystyle 256b^7=23$

$\displaystyle 256^7=\frac{23}{256}$

$\displaystyle b=\sqrt[7]{\frac{23}{256}}$ which is $\displaystyle b=4.7$

Thus, $\displaystyle y=256(4.7)^{x}$

2. Originally Posted by mt_lapin
Find an approximate equation $\displaystyle y=ab^{x}$ of the exponential curve that contains the given pair of points. Round the value of b to two decimal places.

(0, 256) and (7, 23)

my work:

$\displaystyle 256b^7=23$

$\displaystyle 256^7=\frac{23}{256}$

$\displaystyle b=\sqrt[7]{\frac{23}{256}}$ Mr F says: Correct.

which is $\displaystyle b=4.7$ Mr F says: Time to get a new calculator. The seventh root of 23/256 cannot possibly be greater than 1! I get 0.71, correct to two decimal places.

Thus, $\displaystyle y=256(4.7)^{x}$

I did $\displaystyle \left(\frac{23}{256}\right)^7$ when I should have done $\displaystyle \left(\frac{23}{256}\right)^{1/7}$ ... I made a mistake.