The signal strength, SSS milliwatts, of a deep-space communications beam as it penetrates a nebulous gas cloud of density ρ\rhoρ kg m−3^{-3}−3 is modeled by the equation
S=240e−0.075ρ S = 240e^{-0.075\rho} S=240e−0.075ρDetermine an expression for the rate of change of signal strength with respect to density, dSdρ\frac{dS}{d\rho}dρdS.
Select the correct answer from the options below:
dSdρ=−180e−0.075ρ\frac{dS}{d\rho} = -180e^{-0.075\rho}dρdS=−180e−0.075ρ
dSdρ=−18e−0.075ρ\frac{dS}{d\rho} = -18e^{-0.075\rho}dρdS=−18e−0.075ρ
dSdρ=18e−0.075ρ\frac{dS}{d\rho} = 18e^{-0.075\rho}dρdS=18e−0.075ρ
dSdρ=−3200e−0.075ρ\frac{dS}{d\rho} = -3200e^{-0.075\rho}dρdS=−3200e−0.075ρ
375 exam-style questions on AQA A Level Maths 1.10 G: Differentiation, covering 1.10.1 The derivative and second derivative, 1.10.2 Differentiating standard functions, 1.10.3 Applications of differentiation, 1.10.4 Product, quotient and chain rules (A-level only), 1.10.5 Implicit and parametric differentiation (A-level only), and 1.10.6 Constructing differential equations (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.