CCSS.HSA-CED.A.2.Q.UNE.7 - The value of a home in 2015 was $400,000. Its value has been doubling each decade. 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.

Sangeetha Pulapaka (last edited 8 months ago) (Expert, Educator @Qalaxia)

The equation for an exponential function is y = ab^{x} where a is the initial amount,, b is the common growth/decay factor and x is the time, the independent variable.

The output y = v (value in dollars, The initial amount is, a = 400,000, b = 2 (since the value is doubling each decade) and, x = d (time is in decades). The equation will be v = (400,000) \cdot 2^{d}.
When d = -1. v = 400,000 \cdot 2^{-1} = 200,000. This means that a year back, the value was $200,000.
Suppose d = -2, we plug in d = -2, in the equation to get v = 400,000 \cdot 2^{-2} = \frac{400000}{4} = 100,000, and we get the value as v = $100,000. This means that the value of the home in 2013 was $100,000..d=−2 signifies the value of the home 2 years back in 2013