the value of a necklace increases by 3.3% per year. the value of a ring increases by 0.25% per…

the value of a necklace increases by 3.3% per year. the value of a ring increases by 0.25% per month.\nprogress: 0/4\npart 1 of 4\n(a) write a function to represent the value of the ring after t months. use an initial value of $1.\n$a(t) = \\square$

the value of a necklace increases by 3.3% per year. the value of a ring increases by 0.25% per month.\nprogress: 0/4\npart 1 of 4\n(a) write a function to represent the value of the ring after t months. use an initial value of $1.\n$a(t) = \\square$

Answer

Explanation:

Step1: Identify growth type

This is exponential growth, where the value increases by a fixed percentage each period. The general form for exponential growth is $A(t) = P(1 + r)^t$, where $P$ is the initial value, $r$ is the monthly growth rate, and $t$ is time in months.

Step2: Define given values

Initial value $P = 1$, monthly growth rate $r = 0.25% = 0.0025$.

Step3: Substitute into formula

Replace $P$ and $r$ in the general growth formula. $A(t) = 1(1 + 0.0025)^t$

Step4: Simplify the expression

Simplify the base of the exponent. $A(t) = (1.0025)^t$

Answer:

$A(t) = (1.0025)^t$