Question

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!

Answer 1

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