SOLUTION: Given that y=ax^n - 23 and that y=4 when x=3 and y=220 when x=9 find the value of a and n.

Question 818780: Given that y=ax^n - 23 and that y=4 when x=3 and y=220 when x=9 find the value of a and n.
Answer by LinnW(1048) (Show Source): You can put this solution on YOUR website!
Given that y=ax^n - 23 and that y=4 when x=3 and y=220 when x=9 find the value of a and n.
y=ax^n - 23 and that y=4 when x=3 and y=220 when x=9 find the value of a and n.
4 = a(3)^n
and
220 = a(9)^n
Let's solve each equation for a
4 = a(3)^n
divide each side by (3)^n an we have

Similarly 220 = a(9)^n can be written

Setting the right hand sides to be equal,
=
Taking the cross products we have
=
Divide each side by 4
=or=
Divide each side by
= =or =
= =So,=
Take the log of each side
=so, =
Divide each side by log(3)
==3.647632
Now substitute in ,,
a=0.072727
Let's check the second equation, 220 = a(9)^n
220 ?= (0.072727)(9^3.647632)
220 ?= (0.072727)(3025.001)
= 219.9992 So considering rounding error we seem to be correct.
RELATED QUESTIONS
Given that y=ax^n-23, and that y=4 when x=3 and y=220 when x=9,find the value of a and of (answered by rothauserc)

Given that y = ax^b and that y = 5 when x = 2 and y = 29 when x = 4, find the value of a... (answered by stanbon)

A function y is of the form y = ax^n + bx where a, b and n are real numbers. When x is... (answered by Fombitz)

The equation of curve is y=ax^n. Given that the points (2,9) and (3,4) lie on the curve,... (answered by scott8148)

Hi need help on this question The variables x and y are connected by the equation y=... (answered by Theo)

Given that dy/dx=a/x^2+1 and that when x=1 dy/dx=3 and y=3 find the value of y when... (answered by solver91311)

Given that dy/dx=a/x^2 +1 and that when x=1 dy/dx=3 and y=3 find the value of y when... (answered by solver91311)

Given that :3x power 4 *(2x) power 3 over 12x power-2 =Ax power n where A and n are... (answered by ankor@dixie-net.com)

The value of a polynomial ax+by is 7 when x=3 and y=2, and is -3 when x=1 and y=2. Find a (answered by TimothyLamb)