contestada

In the year 1985, a house was valued at $110,000. By the year 2005, the value had appreciated to $145,000. What was the annual growth rate between 1985 and 2005? Assume that the value continued to grow by the same percentage. Write an function that models the exponential growth in the house's value in dollars V over time t. Do not include commas or V(t)= in your answer. Round your b value to 4 decimal places.

Respuesta :

Answer: V(t)=[tex]11000e^{0.0138t}[/tex]

Step-by-step explanation:

Now, the Value, V(t) at any time will depend on the initial value of the house, given as [tex]V_{0}[/tex].

The function that models the exponential growth of the house value in dollars at any time is given (from idea of Depreciation and Calculus) as:  V(t)=[tex]V_{0}e^{rt}[/tex] where r=rate and t=time in years,

In 1985 [tex]V_{0}[/tex]=$110,000, t=0

In 2005, t=20 i.e 20 years after, and V(t)=$145,000

V(t)=[tex]V_{0}e^{rt}[/tex]

145000=[tex]110000e^{r X 20}[/tex]

[tex]e^{r X 20}[/tex]= [tex]\frac{145000}{110000}[/tex]

Taking the natural logarithm of both sides

20r= ln [tex]\frac{145000}{110000}[/tex]

r= [tex]\frac{0.2762}{20}[/tex]=0.01381

The function that models this particular growth is:

V(t)=[tex]11000e^{0.0138t}[/tex]

Answer: 110000(1.0139)^t

Step-by-step explanation:

Otras preguntas