Given An Exponential Function For Compounding Interest, A(X) = P(1.04)x, What Is The Rate Of Change?

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Mathematics

OpenStudy (anonymous):

Given an exponential function for compounding interest, A(10) = P(i.04)x, what is the rate of change?

vii years ago

OpenStudy (campbell_st):

find the 1st derivative... thats the rate of change in futurity value A with respect to fourth dimension x

seven years ago

OpenStudy (anonymous):

in this equation, is 1.04 what yous're using as the slope? @nincompoop

7 years ago

OpenStudy (campbell_st):

at present, 1.04 is the base of the exponent

seven years ago

OpenStudy (anonymous):

I still don't sympathize... im pitiful. this chapter confuses me

7 years agone

OpenStudy (campbell_st):

ok... do you know how to differentiate an exponential office...?

7 years ago

OpenStudy (anonymous):

is that where you practise the log?

7 years agone

OpenStudy (campbell_st):

if \[y = e^{f(x)}\] then \[y' = f'(x) \times e^{f(10)}\]

7 years agone

OpenStudy (campbell_st):

nope its not logs...

seven years agone

OpenStudy (anonymous):

yeah I don't know any of this...

7 years ago

OpenStudy (campbell_st):

ok.... take you washed any calculus...?

7 years agone

OpenStudy (anonymous):

no this is algebra 2

seven years ago

OpenStudy (campbell_st):

ok.... then take makes it hard... accept you been given any information such as ten = 0 A = $5000, then x = 10 A = 7401... anything like that?

7 years ago

OpenStudy (nincompoop):

the involvement rate would exist 0.04 or 4%

7 years ago

OpenStudy (nincompoop):

may I, @campbell_st ?

7 years ago

OpenStudy (campbell_st):

ok....lol... I just realised

vii years agone

OpenStudy (nincompoop):

and so we get-go accept to know the formula for compounded involvement in terms of menstruum. future value = present value * (1+ involvement)^(number of menstruum)

7 years agone

OpenStudy (anonymous):

that sounds familiar @nincompoop

7 years ago

OpenStudy (nincompoop):

A(x) = P(1.04)ten A(x) volition be your future value P is the nowadays value (i.04) is your (1 + interest charge per unit) ^x volition be the terms or how many times it will needed to be applied interest charge per unit is your rate of alter considering it determines how much the corporeality will be compounded

7 years agone

OpenStudy (nincompoop):

since you were given P(1.04)^x it means that the involvement would be ane.04 - 1

7 years agone

OpenStudy (anonymous):

just isn't the rate/compound(due north) ? @nincompoop

7 years ago

OpenStudy (campbell_st):

lol... the interest rate is the rate of change... % per annum... or % per year

vii years ago

OpenStudy (bearding):

ohhh okay! I empathise now!

7 years ago

OpenStudy (bearding):

cheers and then much boys :) @campbell_st @nincompoop

seven years ago

OpenStudy (nincompoop):

the exponent x simply determines the period. significant how long volition this compounded involvement will exist practical. 1 year, 2 years ten years etc.

7 years ago

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