The first difference of the logarithm of Y subscript t equals: a. the growth rate of Y exactly. b. approximately the growth rate of Y when the growth rate is small. c. the first difference of Y. d. the difference between the lead and the lag of Y.

The linear plot of the exponential growth functions with the same 𝑟 value but different 𝑆0 values shows that the function with the larger 𝑆0 value is growing faster.However, the plot on the logarithmic scale for the y-axis (log plot) of the exponential growth functions with the same 𝑟 value but different 𝑆0 values appears to show both functions growing at the same speed, as the two functions are represented by parallel straight lines.Why does the log plot in fact show the function with the larger 𝑆0 value to be growing faster? Select the most appropriate answer.Group of answer choicesEach interval between ticks on a log scale represents an order of magnitude change in the value of the function, so an interval further up the y-axis represents a greater change in the value of the function than an interval lower down the y-axis.Each tick on a log scale represents an additive change in the value of the function, whereas each tick on a linear scale represents a multiplicative ('fold') change in the value of the function.A increasing function with a larger initial value will always grow faster than an increasing function with a smaller initial value.A log scale uniformly compresses the y-axis, so a function that starts higher up the y-axis will be growing faster than one that starts lower down the y-axis.

Which of the following functions grows the fastest?A.𝑎(𝑡)=𝑡52a(t)=t 25​ B.𝑐(𝑡)=𝑡2−5𝑡c(t)= t 2 −5t​ C.𝑖(𝑡)=ln⁡(𝑡100)i(t)=ln(t 100 )D.𝑒(𝑡)=𝑒e(t)=eE.𝑔(𝑡)=3𝑡2−𝑡g(t)=3t 2 −t

Which equation correctly represents the change in output per worker (ΔY), given output per worker (Y), savings rate (s), population growth rate (n), depreciation rate (δ), and technological progress rate (g)?A.ΔY = sY - (n + δ + g)YB.ΔY = sY - (n + δ)Y - gYC.ΔY = sY - (n - δ)Y + gYD.ΔY = sY + (n - δ)Y - gY

Which of the following functions grows the LEAST?A.𝑔(𝑡)=3𝑡2−𝑡g(t)=3t 2 −tB.𝑐(𝑡)=𝑡2−5𝑡c(t)= t 2 −5t​ C.𝑒(𝑡)=𝑒e(t)=eD.𝑎(𝑡)=𝑡52a(t)=t 25​ E.𝑖(𝑡)=ln⁡(𝑡100)i(t)=ln(t 100 )

Exponential growth and decay functions are written in standard form as F(t) = A0 • bkt, where A0 is an initial amount, b is the growth factor, k is the growth rate, and t is _____.A.totalB.timeC.temperatureD.altitudeSUBMITarrow_backPREVIOUS