If we know that delta(t) = 4/(t+3), then calculate a(t).

[Junko85]

Can somebody please help me with the following problem?

\(\displaystyle 3.\, \mbox{ If we know }\, \delta(t)\, =\, \dfrac{4}{t\, +\, 3},\, \mbox{ then calculate }\, a(t).\)

\(\displaystyle a.\, \left(\dfrac{t\, +\, 3}{3}\right)^4\)

\(\displaystyle b.\, 4\, \ln\left(\dfrac{t\, +\, 3}{3}\right)\)

\(\displaystyle c.\, e^{\left(\dfrac{4}{t\, +\, 3}\right)}\)

\(\displaystyle d.\, \ln\left(\dfrac{t\, +\, 3}{4}\right)\)

\(\displaystyle e.\, e^{\left(\dfrac{t\, +\, 3}{4}\right)}\)

What is the correct answer, and how to solve it?

Regards,

 

[Deleted member 4993]

I don't understand this problem, what is the correct answer & how to solve it.

Please help

Best Regards.

What does (t+3)' mean?

How does \(\displaystyle \delta (t)\) relate to a(t)?

 

[Junko85]

What does (t+3)' mean?

How does \(\displaystyle \delta (t)\) relate to a(t)?

It's a multiple choice problem...

 

[Deleted member 4993]

It's a multiple choice problem...

That is obvious! But:

What does (t+3)' mean?

How does [FONT=MathJax_Math]δ[/FONT][FONT=MathJax_Main]([/FONT][FONT=MathJax_Math]t[/FONT][FONT=MathJax_Main])[/FONT]δ(t) relate to a(t)?

and what did you try & get?

 

[Junko85]

Any reason for posting this in the Finance/Business section?

It's not explained. All I know is that it is a financial math problem because it appears in that test module for actuary (financial math section). They could be related as as some kind of differential and integral ...

I'm guessing that \(\displaystyle \,\delta(t)\,\)is related to force of interest and \(\displaystyle \, a(t)\,\) is an amount function. Look, starting on page 28, at this University of Texas PDF.

 

[stapel]

Any reason for posting this in the Finance/Business section?

All I know is that it is a financial math problem because it appears in that test module for actuary (financial math section).

Being on a test for actuarial skills only means that the mathematics being tested is, in some manner, related to or required by the actuarial field. I'll bet that an actuary has to add to whole numbers from time to time. Does this mean that primary-school arithmetic is "Finance/Business Math"? No. And the same can be said for what you have posted.

It's not explained.... They could be related as as some kind of differential and integral. I'm guessing that \(\displaystyle \,\delta(t)\,\)is related to force of interest and \(\displaystyle \, a(t)\,\) is an amount function. Look, starting on page 28, at this University of Texas PDF.

If they don't define their terms, it is difficult, perhaps impossible, to proceed. But if you feel that you have found the correct definition, then please reply with your thoughts and efforts based on that information.

Please be complete. Thank you!

 

[Junko85]

Being on a test for actuarial skills only means that the mathematics being tested is, in some manner, related to or required by the actuarial field. I'll bet that an actuary has to add to whole numbers from time to time. Does this mean that primary-school arithmetic is "Finance/Business Math"? No. And the same can be said for what you have posted.


If they don't define their terms, it is difficult, perhaps impossible, to proceed. But if you feel that you have found the correct definition, then please reply with your thoughts and efforts based on that information.

Please be complete. Thank you!

Confirmed! δ(t) is a force of interest and a(t) is the accumulation function / amount function. Both are related in this way : δ(t) = a'(t) / a(t) = d / dt * (ln (a(t)).

 

[stapel]

\(\displaystyle 3.\, \mbox{ If we know }\, \delta(t)\, =\, \dfrac{4}{t\, +\, 3},\, \mbox{ then calculate }\, a(t).\)

δ(t) is a force of interest and a(t) is the accumulation function / amount function. Both are related in this way:

δ(t) = a'(t) / a(t) = d / dt * (ln (a(t))

Okay. You've been given the function:

. . . . .\(\displaystyle \delta(t)\, =\, \dfrac{a'(t)}{a(t)}\, =\, \dfrac{d}{dt}\, \ln(a(t))\, =\, \dfrac{4}{t\, +\, 3}\)

Then, working from calculus, what can you say about the following?

. . . . .\(\displaystyle \ln(a(t))\, =\, \)\(\displaystyle \displaystyle \int\, \dfrac{4}{t\, +\, 3}\, dt\)

Where might this result lead? If you get stuck, please reply showing your work so far. Thank you!

 

[Junko85]

Okay. You've been given the function:

. . . . .\(\displaystyle \delta(t)\, =\, \dfrac{a'(t)}{a(t)}\, =\, \dfrac{d}{dt}\, \ln(a(t))\, =\, \dfrac{4}{t\, +\, 3}\)

Then, working from calculus, what can you say about the following?

. . . . .\(\displaystyle \ln(a(t))\, =\, \)\(\displaystyle \displaystyle \int\, \dfrac{4}{t\, +\, 3}\, dt\)

Where might this result lead? If you get stuck, please reply showing your work so far. Thank you!

What about the prime in the denominator? What does that mean?

 

[stapel]

What about the prime in the denominator? What does that mean?

What prime in which denominator?

 

[Junko85]

What prime in which denominator?

it's not there because the admin edited my post.. but if you look at the second post of this thread,,, it's there. The Notation for differentiation, the prime in the denominator...(t + 3)'
[h=1][/h][h=1][/h]

 

[Deleted member 4993]

it's not there because the admin edited my post.. but if you look at the second post of this thread,,, it's there. The Notation for differentiation, the prime in the denominator...(t + 3)'

I believe that comma (,) - is a punctuation mark!!

 

[Junko85]

I believe that comma (,) - is a punctuation mark!!

As i said, it wasn't me who wrote that comma, it was edited by the admin, the original post was in pic format (see the second post in this thread by Subhotosh Khan ) and it was written there as a prime (notation for differentiation).