Respuesta :
Answer: it will take 13 years for the home to be valued at 250,000
Step-by-step explanation:
The growth rate is exponential. We would apply the formula for exponential growth which is expressed as
y = b(1 + r)^ t
Where
y represents the value of the house after t years.
t represents the number of years.
b represents the initial value of the house.
r represents rate of growth.
From the information given,
b = 160000
y = 250000
r = 3.5% = 3.5/100 = 0.035
Therefore
250000 = 160000(1 + 0.035)^t
250000/160000 = (1.035)^t
1.5625 = (1.035)^t
Taking log of both sides to base 10
Log 1.5625 = log1.035^t = tlog1.035
0.1938 = t × 0.0149
t = 0.1938/0.0149
t = 13 years
Answer:
In 13 years the home to be valued at 250,000.
Step-by-step explanation:
Present value of home = 160000
Annual increasing rate of the home = 3.5 %
Final value of home is = 250000
Let this value of home becomes after t years.
⇒ [tex]250000 = 160000 (\frac{103.5}{100})^{T}[/tex]
⇒ 1.5625 = [tex]1.035^{T}[/tex]
⇒ ㏑ 1.5625 = T ㏑ 1.035
⇒ T = 13 years
Therefore in 13 years the home to be valued at 250,000.
