Question

table of values
x | y
0 | 1
1 | 3
2 | 9
3 | 27
4 | 243
jack is trying to figure out a rule for this table. he comes to the conclusion that the rule is f(x)= 3^x. why is jack’s rule incorrect?
a 3^4 ≠ 243
b 3^3 ≠ 27
c 3^2 ≠ 9
d 3^1 ≠ 3
e 3^0 ≠ 1

Explanation:

Step1: Check \(3^4\) value

Calculate \(3^4\). By exponent rule, \(3^4 = 3\times3\times3\times3 = 81\).

Step2: Compare with table

In the table, when \(x = 4\), \(y = 243\). But \(3^4 = 81
eq243\), so Jack's rule \(f(x)=3^x\) is incorrect here.

Step3: Analyze options

• Option A: \(3^4

eq243\) (matches our finding).

• Option B: \(3^3 = 27\), so \(3^3 = 27\) is true, eliminate.
• Option C: \(3^2 = 9\), true, eliminate.
• Option D: \(3^1 = 3\), true, eliminate.
• Option E: \(3^0 = 1\), true, eliminate.

Answer:

A. \(3^4
eq243\)