Algebra 1 Question

Question

The present value of an antique is $200. The value of the antique 4 years ago was $189.50 and increases every year by a constant factor, p. Which equation represents the scenario correctly?

A. 200(4)^p = 189.50

B. 200(p)⁴ = 189.50

C. 189.50(4)^p = 200

D. 189.50(p)⁴ = 200

Answer 1

This is an exponential growth type of question.

Recall the formula for exponential growth.

y = a(1+r)^t

y = value at a certain time (in this case, now)

a = initial value

r = growth rate

t = time elapsed

The question mentions a constant factor p, which is going to be 1 plus the growth rate (1+r). The initial value a is 189.50. The final value y is 200, and the time elapsed t is 4 years. Therefore, the equation representing the scenario is 189.50(p)⁴ = 200, or D.

Answer 2

D)

general formula is

A=P(1+r)^t

where P = starting value= $189.50

A = ending value= $200

r = rate of increase =1+r = p

t = time = years=4

200= 189.5(p)^4