Question

A townhouse in San Francisco was purchased for $80,000 in 1975. The appreciation of the building is modeled by the equation: A=80000(1.12)^t, where t represents time in years.
In what year was the building worth double it’s value in 1975?


Year:

Answer 1

Answer:

In 1981 was the building worth double it’s value.

Step-by-step explanation:

Given : A townhouse in San Francisco was purchased for $80,000 in 1975. The appreciation of the building is modeled by the equation : $A=80000(1.12)^t$, where t represents time in years.

To find : In what year was the building worth double it’s value in 1975?

Solution :

The amount is $80,000.

The building worth double it’s value in 1975.

i.e. amount became A=2(80000).

Substitute in the model,

$2(80000)=80000(1.12)^t$

$(1.12)^t=\frac{2(80000)}{80000}$

$(1.12)^t=2$

Taking log both side,

$t\log (1.12)=\log 2$

$t=\frac{\log 2}{\log (1.12)}$

$t=6.11$

i.e. Approx in 6 years.

So, 1975+6=1981

Therefore, in 1981 was the building worth double it’s value.