Question

ASAP

1. Determine the amount of money you will have if you deposit $15,000 compounded quarterly for 5 years at 6% annual interest.



$15,159.26


$245,498.06


$20,202.83


$11,137.06



2.

In the United States, there were approximately 2.23 million marriages in 2005, compared to 2.28 million in 2004. Use an exponential function to predict the number of marriages in 2025, and discuss the reasonableness of the result.



1.46 million: reasonable


3.55 million; exponential models are useful short-term, but not long-term: not reasonable.


1.46 million; exponential models are useful short-term, but not long-term: not reasonable.


1.43 million; exponential models are useful short-term, but not long-term: not reasonable.

Answer 1

∵ Exponential formula is,

`A=P(1+(r)/(n))^(nt)`

Where,

A = Final value,

P = initial value,

r = annual change rate of interest,

t = number of periods per year

First question :

P = $ 15,000

t = 5 years,

r = 6 % = 0.06,

n = 4

Thus, the future amount would be,

`A=15000(1+(0.06)/(4))^(20)`

`=\$ 20202.8250983`

`\approx \$ 20202.83`

Second question :

A = 2.28, if t = 0 year ( assume reference year is 2004 ), n = 1 ( let the number of marriages decrease per year )

`\implies 2.28 = P(1+(r)/(1))^0\implies P = 2.23`

A = 2.23, t = 1,

`\implies 2.23 = 2.28 ( 1+r )^1\implies 2.23 = 2.28 + 2.28r\implies r \approx -(0.05)/(2.28)`

Hence, the function that represents the marriages after x years since 2004,

`A=2.28(1 -(0.05)/(2.28))^x`

If x = 21 years ( i.e. on 2025 )

Population in 2025 would be,

`A=2.28(1- (0.05)/(2.28))^(21)=1.4312160043\approx 1.43\text{ million}`

Hence, the correct option is,

1.43 million; exponential models are useful short-term, but not long-term: not reasonable.