You would like to describe an account th...

题目

You would like to describe an account that begins at TIME(0) = $100.00 and compounds continuously at 9.0% per annum. What is a function that characterizes the value of this account ,A(t), over time according to such a continuous and constant growth trend?

选项

A.A(t)=$100*e^(0.090*TIME(t))

B.ln[A(t)]=ln($100)+0.09*TIME（t）

C.Neither (A) nor (B)

D.Both (A) and (B)

答案

D

解析

A(t)=β(0)＋ e^{β(1)×TIME(t)} describes an exponential (aka, log-linear) trend that is growing at a continuous rate of β(1); in this case, β(0) is the initial value of $100.00 and β(1) is the growth rate of 9.0%. Then we can also take the natural log of both sides and observe thatLN[A(t)] is a linear function of time:LN[A(t)]=LN(β(0)×e^{β(1)×TIME(t)} ）= LN[β(0)] ＋LN(e^{β(1)×TIME(t)} ）= LN[β(0)]＋ β(1)×TIME(t) ）.