A scuba diver is moving underwater when it decides to dive deeper into the water. The depth, D, in meters of the scuba diver t minutes after the dive is represented by the function D(t)=70+45t What is the depth of the scuba diver when it starts to dive deeper?(1 point) Responses 25 meters 25 meters 115 meters 115 meters 70 meters 70 meters 45 meters
The depth of the scuba diver when it starts to dive deeper can be found by substituting t = 0 into the function D(t).
D(0) = 70 + 45(0)
D(0) = 70
Therefore, the depth of the scuba diver when it starts to dive deeper is 70 meters.
To determine the depth of the scuba diver when it starts to dive deeper, we need to find the value of t when D(t) changes from increasing to decreasing.
Given that the function representing the depth is D(t) = 70 + 45t, we can see that the coefficient of t (45) is positive. This means that the depth is initially increasing.
For the depth to start decreasing, the coefficient of t must become negative. This happens when t is larger than 0 (t > 0).
Therefore, the scuba diver starts to dive deeper at t = 0.
To find the depth at that moment, we substitute t = 0 into the function D(t):
D(0) = 70 + 45(0)
D(0) = 70
Hence, the depth of the scuba diver when it starts to dive deeper is 70 meters.
To find the depth of the scuba diver when it starts to dive deeper, we need to determine the value of 't' at that moment.
The function representing the depth, D, of the scuba diver is given as:
D(t) = 70 + 45t
Since the scuba diver starts to dive deeper, it means the depth increases from the initial value. Thus, we need to find the value of 't' when D(t) starts to increase.
The initial depth is given as 70 meters, which means at t = 0 minutes, the scuba diver is already 70 meters deep. To find the point when the scuba diver starts to dive deeper, we need to find the point where D(t) exceeds 70 meters.
Let's set up an equation and solve it:
70 + 45t > 70
Subtracting 70 from both sides, we get:
45t > 0
Dividing both sides by 45, we get:
t > 0
Since the function D(t) = 70 + 45t is continuous and increases with time, the scuba diver starts to dive deeper at t > 0 minutes.
Therefore, the depth of the scuba diver when it starts to dive deeper is 70 meters.