Question

determine whether $5n^2$ or $3^n$ will have the greater value when: 1. $n = 1$ 2. $n = 3$ 3. $n = 5$

Explanation:

1. When \( n = 1 \)

Step 1: Calculate \( 5n^2 \)

Substitute \( n = 1 \) into \( 5n^2 \), we get \( 5\times1^2 = 5\times1 = 5 \).

Step 2: Calculate \( 3^n \)

Substitute \( n = 1 \) into \( 3^n \), we get \( 3^1 = 3 \).

Step 3: Compare the two results

Since \( 5>3 \), \( 5n^2 \) has a greater value.

2. When \( n = 3 \)

Step 1: Calculate \( 5n^2 \)

Substitute \( n = 3 \) into \( 5n^2 \), we get \( 5\times3^2 = 5\times9 = 45 \).

Step 2: Calculate \( 3^n \)

Substitute \( n = 3 \) into \( 3^n \), we get \( 3^3 = 27 \).

Step 3: Compare the two results

Since \( 45>27 \), \( 5n^2 \) has a greater value.

3. When \( n = 5 \)

Step 1: Calculate \( 5n^2 \)

Substitute \( n = 5 \) into \( 5n^2 \), we get \( 5\times5^2 = 5\times25 = 125 \).

Step 2: Calculate \( 3^n \)

Substitute \( n = 5 \) into \( 3^n \), we get \( 3^5 = 243 \).

Step 3: Compare the two results

Since \( 125<243 \), \( 3^n \) has a greater value.

Answer:

1. When \( n = 1 \), \( 5n^2 \) (value 5) is greater than \( 3^n \) (value 3).
2. When \( n = 3 \), \( 5n^2 \) (value 45) is greater than \( 3^n \) (value 27).
3. When \( n = 5 \), \( 3^n \) (value 243) is greater than \( 5n^2 \) (value 125).