Respuesta :
Answer:
Michelle's age = 16
Step-by-step explanation:
As we know,
Amount = [tex]P (1 + r)^{t}[/tex] where
P = Principal amount
r = rate of interest
t = time
Given ,
P = $1000
r = 4.5 % = [tex]\frac{4.5}{100} = 0.045[/tex]
Now,
Given that Amount reaches more than $2000
⇒[tex]P (1 + r)^{t}[/tex] > 2000
⇒[tex]1000(1 + 0.045)^{t}[/tex] > 2000
⇒[tex](1.045)^{t}[/tex] > 2
Now,
we put the value of t from 0 , 1, 2, ..... untill the above equation does not satisfy
Now,
for t = 0
[tex](1.045)^{0} = 1 \ngeq 2[/tex]
for t = 1
[tex](1.045)^{1} = 1.045 \ngeq 2[/tex]
for t = 2
[tex](1.045)^{2} = 1.092 \ngeq 2[/tex]
for t = 3
[tex](1.045)^{3} = 1.14 \ngeq 2[/tex]
for t = 4
[tex](1.045)^{4} = 1.19 \ngeq 2[/tex]
for t = 5
[tex](1.045)^{5} = 1.25 \ngeq 2[/tex]
for t = 6
[tex](1.045)^{6} = 1.30 \ngeq 2[/tex]
for t = 7
[tex](1.045)^{7} = 1.36 \ngeq 2[/tex]
for t = 8
[tex](1.045)^{8} = 1.42 \ngeq 2[/tex]
for t = 9
[tex](1.045)^{9} = 1.48 \ngeq 2[/tex]
for t = 10
[tex](1.045)^{10} = 1.55 \ngeq 2[/tex]
for t = 11
[tex](1.045)^{11} = 1.62 \ngeq 2[/tex]
for t = 12
[tex](1.045)^{12} = 1.69 \ngeq 2[/tex]
for t = 13
[tex](1.045)^{13} = 1.77 \ngeq 2[/tex]
for t = 14
[tex](1.045)^{14} = 1.85 \ngeq 2[/tex]
for t = 15
[tex](1.045)^{15} = 1.93 \ngeq 2[/tex]
for t = 16
[tex](1.045)^{16} = 2.02 > 2[/tex]
It satisfies at t= 16
∴ we get
Michelle's age = 16
