Question

Given an exponential function for compounding interest, A(x) = P(1.04)x, what is the rate of change?

Answer 1

find the 1st derivative... thats the rate of change in future value A with respect to time x

Answer 2

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

Answer 3

now, 1.04 is the base of the exponent

Answer 4

I still don't understand... im sorry. this chapter confuses me

Answer 5

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

Answer 6

is that where you do the log?

Answer 7

if

\[y = e^{f(x)}\]

then

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

Answer 8

nope its not logs...

Answer 9

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

Answer 10

ok.... have you done any calculus...?

Answer 11

no this is algebra 2

Answer 12

ok.... then take makes it hard... have you been given any information such as

x = 0 A = $5000, then x = 10 A = 7401...

anything like that?

Answer 13

the interest rate would be 0.04
or 4%

Answer 14

may I, @campbell_st ?

Answer 15

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

Answer 16

so we first have to know the formula for compounded interest in terms of period.
future value = present value * (1+ interest)^(number of period)

Answer 17

that sounds familiar @nincompoop

Answer 18

A(x) = P(1.04)x
A(x) will be your future value
P is the present value
(1.04) is your (1 + interest rate)
^x will be the terms or how many times it will needed to be applied

interest rate is your rate of change because it determines how much the amount will be compounded

Answer 19

since you were given P(1.04)^x
it means that the interest would be 1.04 - 1

Answer 20

but isn't the rate/compound(n) ? @nincompoop

Answer 21

lol... the interest rate is the rate of change...

% per annum... or % per year

Answer 22

ohhh okay! I understand now!

Answer 23

thank you so much boys :) @campbell_st @nincompoop

Answer 24

the exponent x just determines the period. meaning how long will this compounded interest will be applied. 1 year, 2 years 10 years etc.