Hilary Duff purchased a rare unicorn succulent for $36 in the first year & of course she has amazing taste, so it began increasing in value. The value followed a pattern appreciating it's value by 20% each year. Which recursive equation best models the situation?
t(n) = t(n + 1) • (1.2), where t(1) = 30
t(n + 1) = t(n) • (1.2), where t(1) = 36
t(n + 1) = t(n) + (0.2), where t(1) = 36
t(n + 1) = t(n) • (0.2), where t(1) = 30
(n + 1) = t(n) • (1.2), where t(1) = 36
first 36
after that multiply by 1.2
To find the recursive equation that best models the situation, let's break down the given information:
- Hilary Duff bought a unicorn succulent for $36 in the first year.
- The value of the succulent appreciates by 20% each year.
A recursive equation defines a sequence by relating each term of the sequence to a previous term. In this case, we need to find the equation that relates the value of the succulent in one year to the value in the previous year.
Let's consider the first choice:
t(n) = t(n + 1) • (1.2), where t(1) = 30
According to this equation, the value at year n is equal to the value at year n+1 multiplied by 1.2. However, the initial value stated is t(1) = $30, which contradicts the given information that Hilary Duff purchased the succulent for $36 in the first year. Therefore, this equation does not match the situation.
Now let's consider the second choice:
t(n + 1) = t(n) • (1.2), where t(1) = 36
According to this equation, the value at year n+1 is equal to the value at year n multiplied by 1.2. This equation aligns with the given situation since the value of the unicorn succulent increases by 20% each year. Additionally, the initial value t(1) matches the given value of $36. Therefore, this equation, t(n + 1) = t(n) • (1.2), where t(1) = 36, best models the situation.
It is worth noting that the last two choices don't accurately represent the situation since they involve addition and multiplication with 0.2, which doesn't reflect a 20% increase in value over time.