A temperature sensor records voltage (in volts) that depends on the temperature (in…
MATHEMATICS · Multi-part · AP · Calculus AB · Differentiation: Composite, Implicit, and Inverse Functions · Differentiation: Composite, Implicit, and Inverse Functions
Problem
A temperature sensor records voltage V (in volts) that depends on the temperature T (in degrees Celsius) according to V(T)=3T2+1. The temperature in turn varies with time t (in seconds) following T(t)=ln(5t+2).
(a) Write V explicitly as a function of t. No algebraic simplification is needed at this stage.
(b) Derive an expression for dtdV in terms of t. Simplify completely.
(c) Evaluate dtdV at t=4 and state appropriate units.
(d) Interpret the meaning of the value found in part (c) within the context of the sensor’s operation.