Vera studies the extinction of the bear population of Siberia over time. The following function gives the number of bears t years since Vera started tracking it: B(t)=2190*e^(-0.3 t) What is the instantaneous rate of change of the number of bears after 2 years? Choose 1 answer: (A) 1202 years per bear (B) 1202 bears per year (C) -361 years per bear (D) -361 bears per year

Question

Vera studies the extinction of the bear population of Siberia over time. The following function gives the number of bears  t years since Vera started tracking it:  B(t)=2190*e^(-0.3 t) What is the instantaneous rate of change of the number of bears after 2 years? Choose 1 answer: (A) 1202 years per bear (B) 1202 bears per year (C) -361 years per bear (D) -361 bears per year

Bytelearn · Accepted Answer

Differentiate function B(t): To find the instantaneous rate of change, we need to differentiate the function B(t) with respect to t.Apply chain rule: Differentiate B(t) = 2190 * e^(-0.3t) using the chain rule. dB/dt = 2190 * (-0.3) * e^(-0.3t)Calculate derivative at t=2: Now, plug in t = 2 years into the derivative to find the rate of change at that specific time. dB/dt at t = 2 = 2190 * (-0.3) * e^(-0.3*2)Find e^(-0.6): Calculate the value. dB/dt at t = 2 = 2190 * (-0.3) * e^(-0.6)Multiply values: Use a calculator to find the value of e^(-0.6). e^(-0.6) ≈ 0.5488Perform final multiplication: Now multiply the values together. dB/dt at t = 2 ≈ 2190 * (-0.3) * 0.5488Perform the multiplication. dB/dt at t = 2 ≈ -2190 * 0.16464

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