Respuesta :
Answer:
∵ Exponential formula is,
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]
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,
[tex]A=15000(1+\frac{0.06}{4})^{20}[/tex]
[tex]=\$ 20202.8250983[/tex]
[tex]\approx \$ 20202.83[/tex]
Second question :
A = 2.28, if t = 0 year ( assume reference year is 2004 ), n = 1 ( let the number of marriages decrease per year )
[tex]\implies 2.28 = P(1+\frac{r}{1})^0\implies P = 2.23[/tex]
A = 2.23, t = 1,
[tex]\implies 2.23 = 2.28 ( 1+r )^1\implies 2.23 = 2.28 + 2.28r\implies r \approx -\frac{0.05}{2.28}[/tex]
Hence, the function that represents the marriages after x years since 2004,
[tex]A=2.28(1 -\frac{0.05}{2.28})^x[/tex]
If x = 21 years ( i.e. on 2025 )
Population in 2025 would be,
[tex]A=2.28(1- \frac{0.05}{2.28})^{21}=1.4312160043\approx 1.43\text{ million}[/tex]
Hence, the correct option is,
1.43 million; exponential models are useful short-term, but not long-term: not reasonable.
