To determine which equation best describes the weight of the seedling as it grows, let’s analyze the problem step-by-step.
1. Initial Information:
- The seedling weighs 5 grams at time [tex]\( t = 0 \)[/tex] weeks.
- The weight of the seedling doubles every week.
2. Understanding Doubling:
- If the seedling doubles its weight every week, this is an example of exponential growth.
- Exponential growth can be generally modeled by the function [tex]\( W = W_0 \times a^t \)[/tex], where:
- [tex]\( W_0 \)[/tex] is the initial weight.
- [tex]\( a \)[/tex] is the growth factor.
- [tex]\( t \)[/tex] is the time in weeks.
3. Applying the Information:
- Here, [tex]\( W_0 = 5 \)[/tex] grams (initial weight).
- Since the weight doubles every week, the growth factor [tex]\( a = 2 \)[/tex].
4. Setting up the Equation:
- Using the exponential growth formula, we substitute the initial weight and the growth factor:
[tex]\[
W = 5 \times 2^t
\][/tex]
5. Evaluating Other Options:
- Option B: [tex]\( W = 5 + t^2 \)[/tex]
- This suggests linear growth with an additional quadratic term, which does not match our exponential growth scenario.
- Option C: [tex]\( W = 5t^2 \)[/tex]
- This implies polynomial growth of order 2 (quadratic growth), which again does not model the doubling pattern.
- Option D: [tex]\( W = 10^t \)[/tex]
- This suggests exponential growth but with a base of 10, which does not fit the doubling pattern.
6. Conclusion:
- The correct equation that models the doubling of the seedling's weight every week is:
[tex]\[
W = 5 \times 2^t
\][/tex]
Thus, the answer is [tex]\( \boxed{A} \)[/tex].
