The value V of an item t years after it is purchased is V = 15,000e−0.6286t , 0 ≤ t ≤ 10. (a) Use a graphing utility to graph the function. (b) Find the rates of change of V with respect to t when t = 1 and t = 5. (c) Use a graphing utility to graph the tangent lines to the function when t = 1 and t = 5
Rate of Change
The relation between two quantities which displays how much greater one quantity is than another is called ratio.
Slope
The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as:
The value V of an item t years after it is purchased is V = 15,000e−0.6286t , 0 ≤ t ≤ 10. (a) Use a graphing utility to graph the function. (b) Find the rates of change of V with respect to t when t = 1 and t = 5. (c) Use a graphing utility to graph the tangent lines to the function when t = 1 and t = 5
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