Posted by greeny on Tuesday, February 7, 2012 at 10:29pm.
find the exponential function of the form y=ab^x whose graph passes through the points (4,6) and (7,10)
i got a=3.04 and b= 1.185 so my equation is y=3.04(1.185)^4
is this correct?
one more problem. find a power function of the form y=ax^b whose graph passes through the points (2,3) and (10,21)?
this one im quite confused on how to do, can someone show the steps for it and lead me through until the answer? thanks!

math  Reiny, Tuesday, February 7, 2012 at 10:52pm
I agree with your a and b values, but your equation should have an exponent of x , not 4
(probably just a typo)
2nd:
for (2,3) > 3 = a(2^b)
for (10,21) > 21 = a(10^b)
divide them
21/3 = 10^b/2^b
7 = (10/2)^b
7 = 5^b
take log of both sides
log 7 = log (5^b)
log 7 = b log 5
b = log 7/log 5 = appr. 1.209
sub back into 1st equation
a(2^1.206) = 3
a(2.3119) = 3
a = 1.298
so y = 1.298(x^1.209)
check my arithmetic on the last one