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: [tex]1[/tex] week is [tex]7[/tex] days.)

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

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

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

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

Sure! Let's solve the problem step-by-step to determine which function represents the growth of the water hyacinth in the testing pool.

### Problem Understanding:

1. Initial Situation: You start with a 150-gram sample of water hyacinth.
2. Growth Rate: The plant grows at a rate of 7% per day.
3. Time Frame: We are interested in finding the amount of water hyacinth after [tex]$ t $[/tex] weeks (1 week = 7 days).

### Objective:
We need to find a function that describes the amount of water hyacinth in the pool after [tex]$ t $[/tex] weeks.

### Steps to Determine the Function:

1. Daily Growth Factor:
- If a quantity grows by 7% per day, the daily growth factor is [tex]$ 1 + 0.07 = 1.07 $[/tex].

2. Weekly Time Conversion:
- Since 1 week has 7 days, after [tex]$ t $[/tex] weeks, the number of days is [tex]$ 7t $[/tex].

3. Growth Formula:
- The general formula for exponential growth is given by:
[tex]\[
\text{Final amount} = \text{Initial amount} \times (\text{growth factor})^{\text{number of periods}}
\][/tex]
- For our case:
[tex]\[
\text{Amount after } t \text{ weeks} = 150 \times (1.07)^{7t}
\][/tex]

4. Choosing the Correct Function:
- Based on the analysis, the correct function that models the situation is:
[tex]\[
k(t) = 150 \times (1.07)^{7t}
\][/tex]

### Matching to Options:

From the choices given:
- Option D matches our derived formula:
[tex]\[
k(t) = 150 \times (1.07)^{7t}
\][/tex]

Therefore, the function that accurately represents the growth of the water hyacinth in the testing pool over [tex]$ t $[/tex] weeks is Option D.