deondra has a collection of vintage action figures that is worth $250. if the collection appreciates at a…

deondra has a collection of vintage action figures that is worth $250. if the collection appreciates at a rate of 16% per year, which equation represents the value of the collection after 8 years?

deondra has a collection of vintage action figures that is worth $250. if the collection appreciates at a rate of 16% per year, which equation represents the value of the collection after 8 years?

Answer

Explanation:

Step1: Recall the compound - growth formula

The formula for compound growth (or appreciation in this case) is $A = P(1 + r)^{t}$, where:

  • $A$ is the final amount (value after $t$ years).
  • $P$ is the principal amount (initial value).
  • $r$ is the annual growth rate (expressed as a decimal).
  • $t$ is the number of years.

Step2: Identify the values of $P$, $r$, and $t$

  • The initial value of the collection, $P=$250$.
  • The annual appreciation rate, $r = 16%=0.16$.
  • The number of years, $t = 8$.

Step3: Substitute the values into the formula

Substitute $P = 250$, $r=0.16$, and $t = 8$ into the formula $A=P(1 + r)^{t}$. We get $A=250(1 + 0.16)^{8}$, or in terms of the value $V$ (letting $V$ represent the value of the collection after $t$ years), the equation is $V = 250(1.16)^{8}$.

Answer: $V = 250(1.16)^{8}$ (where $V$ is the value of the collection after 8 years)