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 solve this problem, we need to determine the function that describes the growth of the water hyacinth over time. Here's a step-by-step explanation of how we arrive at the correct function:

1. Identify Daily Growth Rate:
- The water hyacinth grows at a rate of 7% per day. This can be written as a growth factor of [tex]$1 + 0.07 = 1.07$[/tex].

2. Convert Daily Growth to Weekly Growth:
- Since we are interested in the growth over weeks, and there are 7 days in a week, we need to find the equivalent weekly growth rate.
- The weekly growth rate is the daily growth rate raised to the power of 7:
[tex]\[
(1.07)^7
\][/tex]
- This exponentiation gives us the compounded growth factor over a week.

3. Write the Function:
- The initial amount of water hyacinth is 150 grams.
- The amount of water hyacinth after [tex]$ t $[/tex] weeks can be represented by multiplying the initial amount by the weekly growth factor raised to the power of [tex]$ t $[/tex]:
[tex]\[
\text{Amount of water hyacinth} = 150 \times (1.07^7)^t
\][/tex]

Therefore, the correct function that describes the amount of water hyacinth in the testing pool [tex]$ t $[/tex] weeks after the sample is introduced is represented by option (D):

[tex]\[
k(t) = 150 \times (1.07^7)^t
\][/tex]

This equation correctly models the exponential growth of the plant based on the weekly compound interest formula for growth.