Question

You are scuba diving at 120 feet below sea level. You begin to ascend at a rate of 4 feet per second.a. Where will you be 10 seconds after you begin your ascension? b. How long will it take to reach the surface?

Answer 1

The ascension can be modeled using the function:

`d(t)=d_0-r\cdot t`

Where d is the number of feet below the sea level at time t (in seconds), d₀ is the initial "depth", and r is the ascension rate.

From the problem, we identify:

`\begin{gathered} r=4\text{ feet per second} \\ d_0=120\text{ feet} \end{gathered}`

Then:

`d(t)=120-4t`

a)

After 10 seconds, we have t = 10:

`\begin{gathered} d(10)=120-4\cdot10=120-40 \\ \\ \Rightarrow d(10)=80\text{ feet} \end{gathered}`

After 10 seconds, we will be 80 feet below sea level.

b)

To find how long will it take to reach the surface, we need to solve the equation d(t) = 0.

`\begin{gathered} d(t)=0 \\ 120-4t=0 \\ 4t=120 \\ \\ \therefore t=30\text{ seconds} \end{gathered}`

We will reach the surface after 30 seconds.