To determine how much taller Plant 2 is than Plant 1 at the end of week 4, let's break down the steps:
1. Identify the heights at week 3:
- Height of Plant 1 at the end of week 3: [tex]\( 4.45 \)[/tex] inches.
- Height of Plant 2 at the end of week 3: [tex]\( 4.6 \)[/tex] inches.
2. Identify the growth rates:
- Growth rate of Plant 1: [tex]\( \frac{1}{4} \)[/tex] inch per week.
- Growth rate of Plant 2: [tex]\( \frac{3}{10} \)[/tex] inch per week.
3. Calculate the heights at the end of week 4:
- For Plant 1: [tex]\( 4.45 + \frac{1}{4} \)[/tex]
[tex]\[
4.45 + 0.25 = 4.7 \text{ inches}
\][/tex]
- For Plant 2: [tex]\( 4.6 + \frac{3}{10} \)[/tex]
[tex]\[
4.6 + 0.3 = 4.9 \text{ inches}
\][/tex]
4. Determine the difference in height:
- Difference in height between Plant 2 and Plant 1 at the end of week 4:
[tex]\[
4.9 - 4.7 = 0.2 \text{ inches}
\][/tex]
Therefore, at the end of week 4, Plant 2 is 0.2 inches taller than Plant 1.
Thus, the answer is:
[tex]\[ \boxed{0.2 \text{ in.}} \][/tex]
