Question

g. i can calculate which type of function (linear vs. exponential) is best in a situation. the grandma plans to when a child is born, grandma decides to put $200 in an account that earns interest. when the child turns 16, the money will be pulled out of the account for the child as a birthday present. grandma is choosing between two options. option 1: an account that grows by 11% each year option 2: an account that grows by $50 every year which account will create the largest birthday present for the child. explain your reasoning

Explanation:

Step1: Analyze Option 1 (Exponential Growth)

The formula for compound interest (exponential growth) is $A = P(1 + r)^t$, where $P = 200$, $r = 0.11$, and $t = 16$. So $A = 200(1 + 0.11)^{16}$. Calculate $(1.11)^{16}\approx 5.31089$, then $A\approx 200\times5.31089 = 1062.18$.

Step2: Analyze Option 2 (Linear Growth)

The formula for linear growth is $A = P + mt$, where $P = 200$, $m = 50$, and $t = 16$. So $A = 200 + 50\times16 = 200 + 800 = 1000$.

Step3: Compare the Two Amounts

Since $1062.18 > 1000$, Option 1 (exponential growth) gives a larger amount.

Answer:

Option 1: An account that grows by 11% each year will create the largest birthday present.