Find the exponential function of the 2 points (3, 7) and (5, 63). Use
the formula f(x) = a(b)”.

We obtained the two exponential functions:

Step-by-step explanation:

As we know that the exponential function is of the form

f(x) = abˣ

Given the points

We know these points belong to the exponential function.

so substituting the values (3, 7) and (5, 63) in the function

putting (3, 7)

y = abˣ  

7 = ab³

also putting (5, 63)

y = abˣ

63 = ab⁵

Considering the 2nd equation

63 = ab⁵

as

so

63 = ab³×b²  

substituting 7 = ab³ in 63 = ab³×b²  

63 = 7 × b²

b² = 63/7

b² = 9

b = ± 3

If b = 3

plug in b = 3 in the equation 7 = ab³ to find the value 'a'

7 = ab³

7 = a(3)³

7 = a × 27

a = 7/27

so, a = 7/27 and b = 3 would give us the function

y = abˣ

if b = -3

plug in b = -3 in the equation 7 = ab³ to find the value 'a'

so, a = -7/27 and b = -3 would give us the function

y = abˣ

Thus, we obtained the two exponential functions:

both equations and proportions are better.

only 10/60 isn't equivalent

hope this : )