Question

if the graph of an exponential function passes through the points (1,6) and (4,48) find an equation of the function

Answer 1

One way is trial and error
equation of exonential is
y=a(b^x)
lets try some stuff
one way is trial and error
after 20 minutes we come up with y=3(2^x)

another way is recognizing that this is a sequence
$a_{n}=a_{1}r^{n-1}$
a1=6, cool
sub
a4=48
$48=a_{4}=6r^{4-1}$
$48=6r^{3}$
dividie everybody by 6
$8=r^{3}$
cube root
2=r

therefor

equation is
f(x)=3(2^x) or y=3(2^x)

Answer 2

When you write an equation of a line, you first have to find the slope. The equation for slope is (y∨2 - y∨1) / (x∨2 - x∨1), so fill that in with your coordinates.

(48 - 6) / (4 - 1)      Subtract your two sets.
42 / 3                     Divide
14               

So, you know the slope of the equation is 14. Now, you fill in the point-slope equation, (y - y∨1) = m(x - x∨1). Fill it in with one set of coordinates and solve.

(y - 6) = 14(x - 1)     Distributive Property
y - 6 = 14x - 14        Add 6 to both sides.
y = 14x - 8