Question 916507: Need help with solving this problem, thank you for helping!
Find the values of the constants C and b so that the curve y = Cb^(x) contains the points (4,3) and (5,6). Express your answers as integers or simplified fractions.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! y = cb^(x) contains the points (4,3) and (5,6)
this means that:
when x = 4, y = 3 and when x = 5, y = 6
when x = 4 and y = 3, your original equation becomes:
3 = cb^4
when x = 5 and y = 6, your original equation becomes:
6 = cb^5
if you take cb^5 and divide it by cb^4, you get:
cb^5/cb^4 = 6/3 = 2
since c/c = 1 and b^5/b^4 = b^(5-4) = b, your equation of cb^5/cb^4 = 2 becomes:
b = 2
go back to the first original equation (either one will be ok), and replace b with 2 to get:
first original equation of 3 = cb^4 becomes:
3 = c*2^4 which becomes:
3 = c*16
divide both sides of this equation by 16 to get:
c = 3/16
your solution should be that b = 2 and c = 3/16
replace c with 3/16 and b with 2 and x with 4 in your first original equation to get:
y = cb^x becomes:
y = 3/16 *2^4 which becomes:
y = 3/16 * 16 which becomes:
y = 3
solution is confirmed to be good in the first equation because y = cb^x becomes y = 3 when x = 4.
replace c with 3/16 and b with 2 and x with 5 in your second original equation to get:
y = cb^x becomes:
y = 3/16 * 2^5 which becomes:
y = 3/16 * 32 which becomes:
y = 6
solution is confirmed to be good in the second equation because y = cb^x becomes y = 6 when x = 5.
your solution is c = 3/16 and b = 2.
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