Be Precise:

A submersible descends to a depth of 1500 feet at a rate of 40 feet per minute to explore an underwater shipwreck.

a. Identify the independent and dependent variables. Then write a function to represent the total depth of the submersible in any number of minutes.

b. Use the equation to find the total amount of time it took to reach 1500 feet.

Sure! Let's solve this step-by-step.

### Part a: Identify Independent and Dependent Variables and Write a Function

1. Identify Variables:
- Independent Variable: Time in minutes (how long the submersible descends).
- Dependent Variable: Depth in feet (how deep the submersible goes).

2. Write a Function:
- The submersible descends at a rate of 40 feet per minute.
- We can express the total depth [tex]\( D(t) \)[/tex] in feet, depending on time [tex]\( t \)[/tex] in minutes, with the function:

[tex]\[
D(t) = 40 \times t
\][/tex]

- Here, [tex]\( D(t) \)[/tex] is the depth and [tex]\( t \)[/tex] is the time in minutes.

### Part b: Calculate Total Time to Reach 1500 Feet

1. Set up the Equation:
- We need to find how much time it takes to reach a depth of 1500 feet.
- Using the function from part a, we set [tex]\( D(t) = 1500 \)[/tex].

[tex]\[
1500 = 40 \times t
\][/tex]

2. Solve for [tex]\( t \)[/tex]:
- Divide both sides by 40 to solve for [tex]\( t \)[/tex]:

[tex]\[
t = \frac{1500}{40}
\][/tex]

- Calculate the result:

[tex]\[
t = 37.5
\][/tex]

The total amount of time it took the submersible to reach a depth of 1500 feet is 37.5 minutes.