Water hyacinth is an invasive plant species found in many lakes that typically grows at a rate of [tex]$7\%$[/tex] per day. As part of a study, a scientist introduces a 150-gram sample of water hyacinth into a testing pool. Which of the following functions gives the amount of water hyacinth in the testing pool [tex]$t$[/tex] weeks after the sample is introduced? (Note: 1 week is 7 days.)

A. [tex]f(t) = 150\left(1 + 0.07^{(1/7)}\right)^t[/tex]

B. [tex]g(t) = 150\left(1.07^{(1/7)}\right)^t[/tex]

C. [tex]h(t) = 150\left(1 + 0.07^{(7)}\right)^t[/tex]

D. [tex]k(t) = 150\left(1.07^{(7)}\right)^t[/tex]

To determine the correct function that represents the growth of the water hyacinth in the testing pool over time, let's break down the information and calculations:

1. Initial Information:
- You start with 150 grams of water hyacinth.
- The growth rate of water hyacinth is 7% per day.
- 1 week consists of 7 days.

2. Goal:
- Find the function that gives the amount of water hyacinth, [tex]$ t $[/tex] weeks after it's introduced.

3. Growth Rate Calculation:
- Daily growth factor is [tex]$ 1 + 0.07 = 1.07 $[/tex] because the plant grows by 7% each day.
- To find the growth factor for a week (7 days), we calculate [tex]$ (1.07)^7 $[/tex].

4. Weekly Growth Factor:
- Calculating [tex]$ (1.07)^7 $[/tex] gives approximately 1.6057814764784306. This is the weekly growth factor, meaning that at the end of each week, the amount of water hyacinth is multiplied by this factor.

5. Function Formulation:
- We use the initial mass of the water hyacinth (150 grams) and multiply it by the weekly growth factor raised to the power of [tex]$ t $[/tex] weeks.
- The function is: [tex]$ k(t) = 150 \times (1.07^7)^t $[/tex].

6. Matching with Given Options:
- Option (D) is [tex]$ k(t) = 150 \times (1.07^{7})^t $[/tex].

Therefore, the correct function is option (D):
[tex]\[ k(t) = 150 \left(1.07^{7}\right)^t \][/tex]

This function correctly represents the growth of the water hyacinth in the pool over [tex]$ t $[/tex] weeks.