Question

the value of a home in 2015 was $400,000. its value has been doubling each decade.
part a
if v is the value of the home, in dollars, write an equation for v in terms of d, the number of decades since 2015.
$v = 400000 \cdot 2^d$
part b
what is the value of the home when $d = -1$?

Explanation:

Step1: Identify the formula

We are given the equation for the value of the home \( v = 400000\cdot2^{d} \), and we need to find the value when \( d=- 1 \).

Step2: Substitute \( d = - 1 \) into the formula

Substitute \( d=-1 \) into \( v = 400000\cdot2^{d} \), we get \( v=400000\times2^{-1} \).

Step3: Simplify the expression

Recall that \( a^{-n}=\frac{1}{a^{n}} \), so \( 2^{-1}=\frac{1}{2} \). Then \( v = 400000\times\frac{1}{2} \).

Step4: Calculate the result

\( 400000\times\frac{1}{2}=200000 \).

Answer:

The value of the home when \( d = - 1 \) is \(\$200000\).