Questions: In seawater, the pressure, P , (in psi) is related to the depth, d , (in ft ) according to the function: 1000 P-433 d=14700 (a) Solve this equation to write it in the form: P(d)= (b) The Titanic was discovered at a depth of 12,500 ft. Which of the following function notations states the pressure at the depth of the Titanic? A. P(d)=12,500 B. d=5552.2 C. P(12,500) D. P(d)=5552.2 E. P=12,500 F. P(5552.2) (c) Find the pressure at the depth of 2095 ft . lbs / in^2 (round to two decimal places as needed)

In seawater, the pressure, P , (in psi) is related to the depth, d , (in ft ) according to the function:
1000 P-433 d=14700
(a) Solve this equation to write it in the form: P(d)=
(b) The Titanic was discovered at a depth of 12,500 ft. Which of the following function notations states the pressure at the depth of the Titanic?
A. P(d)=12,500
B. d=5552.2
C. P(12,500)
D. P(d)=5552.2
E. P=12,500
F. P(5552.2)
(c) Find the pressure at the depth of 2095 ft . lbs / in^2
(round to two decimal places as needed)

Transcript text: In seawater, the pressure, P , (in psi) is related to the depth, d , (in ft ) according to the function: \[ 1000 P-433 d=14700 \] (a) Solve this equation to write it in the form: $P(d)=$ $\square$ (b) The Titanic was discovered at a depth of $12,500 \mathrm{ft}$. Which of the following function notations states the pressure at the depth of the Titanic? A. $P(d)=12,500$ B. $d=5552.2$ C. $P(12,500)$ D. $P(d)=5552.2$ E. $P=12,500$ F. $P(5552.2)$ (c) Find the pressure at the depth of 2095 ft . $\square$ $\mathrm{lbs} / \mathrm{in}^{2}$ (round to two decimal places as needed)

Solution

Solution Steps

Solution Approach

(a) To solve the equation $1000P - 433d = 14700$ for $P$ in terms of $d$, isolate $P$ on one side of the equation.

(b) To determine the correct function notation for the pressure at the depth of the Titanic, identify the notation that represents the pressure function evaluated at $d = 12,500$.

(c) To find the pressure at a depth of 2095 ft, substitute $d = 2095$ into the function $P(d)$ derived in part (a) and solve for $P$.

Step 1: Solve the equation for $ P $ in terms of $ d $

Given the equation: \[ 1000P - 433d = 14700 \] we solve for $ P $ in terms of $ d $: \[ 1000P = 433d + 14700 \] \[ P = \frac{433d + 14700}{1000} \] \[ P(d) = 0.433d + 14.7 \]

Step 2: Determine the correct function notation for the pressure at the depth of the Titanic

The Titanic was discovered at a depth of $ 12{,}500 \, \text{ft} $. The correct function notation to represent the pressure at this depth is: \[ P(12{,}500) \] Thus, the correct answer is: \[ \boxed{\text{C. } P(12{,}500)} \]

Step 3: Find the pressure at a depth of $ 2095 \, \text{ft} $

To find the pressure at a depth of $ 2095 \, \text{ft} $, we substitute $ d = 2095 $ into the function $ P(d) $: \[ P(2095) = 0.433 \times 2095 + 14.7 \] \[ P(2095) = 906.135 + 14.7 \] \[ P(2095) = 920.835 \] Rounding to two decimal places, we get: \[ P(2095) \approx 920.84 \, \text{lbs/in}^2 \]