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1.6 Exponentials and Logarithms

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Question 49

An automated trading algorithm is monitoring the growth of a digital asset portfolio. The value of the portfolio, VVV pounds, at time ttt weeks after the algorithm was activated is modelled by the equation

log⁡10V=1.94+0.12t \log_{10} V = 1.94 + 0.12t log10​V=1.94+0.12t
a.

Write this equation in the form V=abtV = ab^tV=abt, where aaa and bbb are constants to be found. Give each value to 4 significant figures.

[3]
b.

When t=Tt = Tt=T, the value of the portfolio is £4000. Find the value of TTT according to the model, giving your answer to 3 significant figures.

[3]
c.

The algorithm is programmed to trigger a 'rebalance' alert if the portfolio value exceeds £5000. Determine whether or not the portfolio will require a rebalance within the first 14 weeks.

[2]

1.6 Exponentials and Logarithms Questions

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