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

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

Answer 2

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)