Question

3. Identify the initial value, a, of the function f (x) = ab^x if its graph passes through the points (1, 6) and (2, 18).

A. 5
B. 3
C. 4
D. 2

Answer 1

The initial value = 2

Hence, option (d) is true.

Explanation:

Consider the function

f(x) = abˣ

Given the points

• (1, 6)

• (2, 18)

substituting (1, 6) in the function

y = abˣ

6 = ab¹

6 = ab

substituting (2, 18) in the function

y = abˣ

18 = ab²

18 = ab×b

18 = 6×b ∵ ab = 6

b = 18/6

b = 3

now substituting b = 3 in 6 = ab

6 = ab

6 = a × 3

a = 6/3

a = 2

In order to determine the initial value, we need to put x = 0 in the function

y = abˣ

putting x = 0

y = ab⁰

as a = 2 and b⁰=1

so substituting a = 2 and b⁰=1

y = 2×1

y = 2

Therefore, the initial value = 2

Hence, option (d) is true.