Algebra Expression Question

Question

The expression 234,000(1.26)^x models the value of a house, where x is the number of years since the house was purchased. What does the value 1.26 represent?

A. The cost of repairs on the house

B. The factor by which the value of the house increases each year

C. The value of the house in ten years

D. The value of the house when it was purchased

Answer 1

This question asks us to apply our knowledge of an exponential model, one of the form P=P₀(r)^t

Definition of the Equation P=P₀(r)^t

1. P is our population at any point in time, what we are trying to predict with our model
2. P₀ is our starting population, or the population at time t=0. The problem tells us this is 234000
3. r is the rate of change in the population within a single time period. The problem tells us this is 1.26
4. t is our dependent variable, what we use to predict P. In this problem it is the number of years that have passed, or the variable x

Another way to express the concept of rate of change is the factor by which the population changes year over year, which leads us to select answer b)

Answer 2

B) is correct

factor by which the house increases in value each year