Question

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Answer 1

Answer:

y = 2 (1.41)x

Step-by-step explanation:

2 = ab0 and 4 = ab2. Since we know that b0 = 1, the first equation becomes 2 = a. Substituting a in the second equation yields 4 = 2b2, which we simplify to b2 = 2, or b = square root of 2, which equals approximately 1.41. The defining function is then y = 2 (1.41)x.

Answer 2

Since 4 = 2² and 16 = 2⁴, we can start off with the function f(x) = 2ˣ.

But then f(0) = 2⁰ = 1 ≠ 4, and f(2) = 2² = 4 ≠ 16.

To account for this, add 2 to the exponent, so that f(x) = 2ˣ⁺².

Now f(0) = 2⁰⁺² = 2² = 4, and f(2) = 2²⁺² = 2⁴ = 16, as required.