Question

A mutual fund is currently valued at $80 per share and its value per share is increasing at a rate of $0.40 a day. Let V=f(t) be the value of the share t days from now.

Express the information given about the mutual fund in terms of f ' (derivitive of f)

Answer 1

V = f(t) = 80(0.004)^t
log f(t) = log(80(0.004)^t) = log(80) + t log(0.004)
1/f(t) f'(t) = log(0.004)
f(t) = f'(t) / log(0.004)

Answer 2

Answer:

The expression of mutual fund in terms of f'(t) is : f(t) = t·f'(t) + 80

Step-by-step explanation:

The current value of the mutual fund = $80 per share

The rate of increase of the share value = $0.40 per day

Let the number of days be t

So, Value of the share t days from now is represented by :

V = f(t) = 0.40·t + 80 .........(1)

Now, we need to express this relation in terms of f'(t)

So, Differentiating the equation (1) with respect to t

⇒ f'(t) = 0.4

Putting this value of 0.4 in the equation (1)

⇒ V = f(t) = t·f'(t) + 80

Hence, The expression of mutual fund in terms of f'(t) is : f(t) = t·f'(t) + 80