Question

From an elevation of 3.5 m below the surface of the water, a northern bottlenose whale dives at the rate of 1.8 m/s. What is a function rule that gives the whale's depth d as a function of time in seconds? What is the depth after 100 seconds?

a) d(t)=3.5−1.8t, d(100)=−175.5 m
b) d(t)=1.8t−3.5, d(100)=175.5 m
c) d(t)=1.8t+3.5, d(100)=183.5 m
d) d(t)=3.5+1.8t,d(100)=183.5 m

Answer 1

The function rule that represents the whale's depth as a function of time is d(t) = 3.5 + 1.8t. After 100 seconds, the depth of the whale will be 183.5 meters.

Step-by-step explanation:

You are asking how to create a function that gives the whale's depth (d) as a function of time (t), taking into account that the whale starts at an elevation of 3.5 meters below the surface and dives at a rate of 1.8 meters per second.

To model this situation, we need an equation that starts with the initial depth (3.5 meters below the surface, which is a positive value since we're considering depth below sea level) and increases the depth by 1.8 meters for every second that passes. This can be expressed as:

d(t) = 3.5 + 1.8t,

where:

• d(t) is the depth in meters after t seconds.
• t is the time in seconds.

After 100 seconds, the depth will be:

d(100) = 3.5 + 1.8(100)

d(100) = 3.5 + 180

d(100) = 183.5 meters

Thus, after 100 seconds, the whale will be at a depth of 183.5 meters.