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
425 exam-style questions on OCR A Level Maths 1.7 Differentiation, covering 1.7.1 Derivative as gradient of the tangent, 1.7.2 Gradient of the tangent at a point, 1.7.3 Sketching the gradient function, 1.7.4 Second derivatives, 1.7.5 Second derivative as rate of change of gradient, 1.7.6 Convex, concave and points of inflection (A-level only), 1.7.7 Differentiation from first principles for powers of x, 1.7.8 Differentiation from first principles for sin x and cos x (A-level only), 1.7.9 Differentiating x^n, 1.7.10 Differentiating e^(kx) and a^(kx) (A-level only), 1.7.11 Differentiating trigonometric functions (A-level only), 1.7.12 Derivative of ln x (A-level only), 1.7.13 Tangents and normals, 1.7.14 Stationary points, 1.7.15 Increasing and decreasing functions, 1.7.16 Points of inflection (A-level only), 1.7.17 Product and quotient rules (A-level only), 1.7.18 Chain rule (A-level only), 1.7.19 Parametric and implicit differentiation (A-level only), 1.7.20 Constructing differential equations (A-level only), and 1.7 Differentiation. Each one has a worked solution and a mark scheme showing where the marks go.