The Power Slide: Watching Exponents Grow
See how a small change in the exponent creates a massive change in the result.
Equation
y = 3^x
Graph
Table
| x | y |
|---|---|
| 0 | 1 |
| 1 | 3 |
| 2 | 9 |
| 3 | 27 |
| 4 | 81 |
| 5 | 243 |
| 6 | 729 |
| 7 | 2187 |
| 8 | 6561 |
What this lesson covers
What you do
You shape the function y = b^x and watch the graph answer.
Challenges to clear
- Set the base b to 2 and find 2^5 in the table — it should be 32.
- Stay at b = 2: one more step in the exponent DOUBLES the value — check 2^6 = 64.
- Powers of 5 now — slide b to 5.
- Then find the multiplier: x = 3 must read 250. Three 5s make 125, so a is 2.
Check yourself
Why does 2^5 (32) grow so much faster than 5^2 (25)?
- In 2^5, the base 2 is multiplied by itself 5 times. — correct
- In 2^5, the exponent 5 is added to the base 2 five times.
- In 5^2, the base 5 is multiplied by itself 2 times.
- In 5^2, the exponent 2 is added to the base 5 two times.
Think about it
- Each step right in the table multiplies y by the base b. If b = 2, what is the jump from x = 5 to x = 6?
- If you increase the base b by 1, what happens to y at x = 4?