You invest $500 @ 6.5% compound annually given by the equation A=500(1.065)ⁿ where n=number of years and A=amount earned.
How long would it take to earn $1000?
1000 = A; n = years.
1000 = 500(1.065)n
1000/500 = 2 = (1.065)n
log 2 = n*log 1.065
0.30103 = n*0.02735
n = 0.30103/0.02735
n=11 years.
wow thanks so much!
what does the log button mean exactly?
what does it do?
The log button provides the logarithm (base 10) of any number punched into the calculator. (There is also an ln button on most calculators that provides the logarithm (base e) of any number punched into the calculator. There is probably a way of solving that equation without using logs but I don't know how to do it. I know that log xy is the same as y*log x and I let the calculator and algebra do the rest. A quick lesson in logs.
The definition of logarithm (I'll use base 10) is the power to which 10 must be raised to give that numbers. Sounds confusing but all it means is that the
log 10 = 1 BECAUSE 101 = 10.
log 100=2 BECAUSE 102 = 100.
log 1000=3 because 103 = 1000 etc. Logs of numbers between 1 and 10 must be looked up on a calculator or in a set of tables since they are not whole numbers like 1 and 2 and 3. Hope this helps.
I have this exact same question, but in my assignment I'm told I have to make a table of values, graph whatever it is, find the x&y intercepts, find the domain and range, determine whether it's increasing or decreasing, the equation of the asymptote, and what is the implication of the asymptote related to caffeine in the body.
* disregard the caffeine comment. sorry about that.
To find out how long it would take to earn $1000 with an investment of $500 at a compound interest rate of 6.5% annually, we can use the given equation:
A = 500(1.065)ⁿ
Here, A represents the total amount earned, and n represents the number of years. We need to find the value of n when A equals $1000.
So, we can set up the equation as follows:
1000 = 500(1.065)ⁿ
To solve for n, we need to isolate the variable n. To do that, let's divide both sides of the equation by 500:
1000/500 = (1.065)ⁿ
2 = (1.065)ⁿ
To get rid of the base 1.065, we can use logarithms. We can apply the logarithm with base 1.065 to both sides of the equation. Let's assume we use the logarithm with base 10 (log10):
log10(2) = log10((1.065)ⁿ)
Using the logarithmic property logb(a^c) = c * logb(a), we can move the exponent n in front of the logarithm:
log10(2) = n * log10(1.065)
Now, divide both sides of the equation by log10(1.065):
n = log10(2) / log10(1.065)
Using a calculator, we can evaluate this expression:
n ≈ 10.09
So, it would take approximately 10.09 years to earn $1000 from an initial investment of $500 at a compound interest rate of 6.5% annually.