Find a function of the form f(x)=Ca^x which passes through the points (3,4) and (5,100) C= A=

Answer 1

The ordered pairs you listed are (x, y) values, so given (3, 4) you can plug into the equation x = 3 and f(x) or y = 4. And you can do the same for (5, 100)

That gives you two different equations:

4 = Ca³

100 = Ca⁵

Divide both sides of the first equation by "a³" and you get C = 4/a³ then, based on that, plug in "4/a³" into the second equation in place of "C":

100 = (4/a³)a⁵

100 = 4a² then solve for "a"

Once you get "a", plug that value into C = 4/a³ to solve for C

Answer 2

4 = Ca^3oints

100 = Ca⁵

25 = a² divice bottom equation by top equation±

±5 = a discard the -5

f(x) = C(5^x)

Can you substitute one of the point and solve for C?