Question

Write an exponential function in the form y=ab^x that goes through points (0,14) and (3,3024).

Answer 1

Answer:

y = 14 $(6)^{x}$

Step-by-step explanation:

For an exponential function of the form y = a$b^{x}$

Use the given points to find a and b

Using (0, 14 ), then

14 = a$b^{0}$ ( $b^{0}$ = 1 ) , thus

a = 14

y = 14$b^{x}$

Using (3, 3024 ) , then

3024 = 14 b³ ( divide both sides by 14 )

216 = b³ ( take the cube root of both sides )

b = $\sqrt[3]{216}$ = 6 , thus

y = 14 × $6^{x}$ ← exponential function