jenny is tracking the monthly sales totals for her boutique. the given piece - wise function represents the…

jenny is tracking the monthly sales totals for her boutique. the given piece - wise function represents the boutiques monthly sales, in dollars, where x represents the number of months since jenny began tracking the data.\nf(x) = {4000(1.1)^x, 0 <= x < 3; 100x + 5024, 3 <= x < 6; -x^2 + 5x + 5630, 6 < x <= 8}\nwhat were the boutiques monthly sales when jenny first began tracking the data?\na. $4400\nb. $5324\nc. $4000\nd. $5616

jenny is tracking the monthly sales totals for her boutique. the given piece - wise function represents the boutiques monthly sales, in dollars, where x represents the number of months since jenny began tracking the data.\nf(x) = {4000(1.1)^x, 0 <= x < 3; 100x + 5024, 3 <= x < 6; -x^2 + 5x + 5630, 6 < x <= 8}\nwhat were the boutiques monthly sales when jenny first began tracking the data?\na. $4400\nb. $5324\nc. $4000\nd. $5616

Answer

Explanation:

Step1: Identify the relevant part of the piece - wise function

When Jenny first began tracking the data, $x = 0$. Since $0\leq x<3$, we use the first part of the piece - wise function $f(x)=4000(1.1)^x$.

Step2: Substitute $x = 0$ into the function

Substitute $x = 0$ into $f(x)=4000(1.1)^x$. According to the exponent rule $a^0 = 1$ for $a\neq0$, we have $f(0)=4000\times(1.1)^0$. Since $(1.1)^0 = 1$, then $f(0)=4000\times1=4000$.

Answer:

C. $4,000$