To determine the heights of Plant B at the same time points given in the table for Plant A, let's follow these steps:
### Step 1: Identify Time Points for Plant A
We are given the time in weeks for Plant A:
[tex]\[ t_A = [60, 80, 100, 120] \][/tex]
### Step 2: Gather Heights for Plant A
We also have the heights in inches for Plant A at these specific times:
[tex]\[ h_A = [90, 120, 150, 180] \][/tex]
### Step 3: Use the Equation for Plant B
For Plant B, we are given the relationship between height [tex]\( h \)[/tex] and time [tex]\( t \)[/tex]:
[tex]\[ h = \frac{4t}{3} \][/tex]
### Step 4: Calculate Heights for Plant B
Now, we need to calculate the heights of Plant B at the same time points as Plant A using the given equation.
For each time point [tex]\( t \)[/tex]:
1. When [tex]\( t = 60 \)[/tex]:
[tex]\[ h_B = \frac{4 \times 60}{3} = 80.0 \][/tex]
2. When [tex]\( t = 80 \)[/tex]:
[tex]\[ h_B = \frac{4 \times 80}{3} \approx 106.67 \][/tex]
3. When [tex]\( t = 100 \)[/tex]:
[tex]\[ h_B = \frac{4 \times 100}{3} \approx 133.33 \][/tex]
4. When [tex]\( t = 120 \)[/tex]:
[tex]\[ h_B = \frac{4 \times 120}{3} = 160.0 \][/tex]
### Step 5: Summarize the Results
We can now summarize the heights of Plant B at the given time points.
[tex]\[
h_B = [80.0, 106.67, 133.33, 160.0]
\][/tex]
### Final Summary
The heights in inches of Plant B at specified times are:
\begin{tabular}{|c|c|c|c|c|}
\hline \multicolumn{5}{|c|}{ Plant B } \\
\hline Time in weeks, [tex]$t$[/tex] & 60 & 80 & 100 & 120 \\
\hline Height in inches, [tex]$h$[/tex] & 80.0 & 106.67 & 133.33 & 160.0 \\
\hline
\end{tabular}
- For [tex]\( t = 60 \)[/tex] weeks, [tex]\( h_B \)[/tex] is 80.0 inches.
- For [tex]\( t = 80 \)[/tex] weeks, [tex]\( h_B \)[/tex] is approximately 106.67 inches.
- For [tex]\( t = 100 \)[/tex] weeks, [tex]\( h_B \)[/tex] is approximately 133.33 inches.
- For [tex]\( t = 120 \)[/tex] weeks, [tex]\( h_B \)[/tex] is 160.0 inches.
This gives the complete evaluation of Plant B's height progression over the same period as Plant A.
