Question

This is matching:#1 If solving a problem with population growth compounding CONTINUOUSLY, which of the following formulas would you use?#2 If solving a problem with population growth compounding ANNUALLY, which of the following formulas would you use?#3 If solving a problem with population growth compounding QUARTERLY, which of the following formulas would you use?#4 If solving a problem with continuously compounding interest, which of the following formulas would you use?A: A(t)=P(1+r÷n)^ntB: A(t)=Pe^rtC: P(t)=P0(1+r)^tD: P(t)=P0^e^rt

Answer 1

#1

The formula for continuous compounding is:

`A(t)=P_{}e^(r\cdot t)`

#2

Since the population grows compounding annually, we have that:

`P(t)=P_0(1+r)^t`

#3

For a problem with population growth compounding quarterly, we have to divide the rate between n=4, therefore:

`A(t)=P(1+(r)/(n))^{n\cdot t^{}}`

#4

Finally, for continuously compounded interest we have the formula:

`P(t)=P_0e^(r\cdot t)`