$N=500(2.3)^{\frac{t}{12}}$ $\newline$ The number of hits, $N$ , a new website obtains $t$ months after it is launched is modeled by the equation shown. By what percent does the number of hits grow in one year? $\newline$ (Ignore the $\%$ symbol when entering your answer. For example, if the answer is $11.2 \%$ , enter $11$ . $2$ .)

Full solution

N=500(2.3)^{\frac{t}{12}}

\newline

The number of hits,

N

, a new website obtains

t

months after it is launched is modeled by the equation shown. By what percent does the number of hits grow in one year?

\newline

(Ignore the

\%

symbol when entering your answer. For example, if the answer is

11.2 \%

, enter

11

2

Given Formula Calculation: We are given the formula for the number of hits $N$ as a function of time $t$ in months: $N = 500(2.3)^{\frac{t}{12}}$ . To find the percent growth in one year, we need to calculate the value of $N$ for $t = 12$ months.
Substitute $t = 12$ : Substitute $t = 12$ into the equation to find the number of hits after one year. $N = 500(2.3)^{\frac{12}{12}} = 500(2.3)^1$
Calculate $N$ after $1$ year: Calculate the value of $N$ after one year. $\newline$ $N = 500 \times 2.3 = 1150$
Initial Number of Hits: Now we need to find the percent growth from the initial number of hits to the number of hits after one year. The initial number of hits when $t = 0$ is $N = 500(2.3)^{0} = 500$ .
Calculate Percent Growth: Calculate the percent growth using the formula: Percent Growth = $[\frac{\text{Final Value} - \text{Initial Value}}{\text{Initial Value}}] \times 100$ . $\newline$ Percent Growth = $[\frac{1150 - 500}{500}] \times 100$
Evaluate Percent Growth: Evaluate the percent growth. $\newline$ Percent Growth = $\left[\frac{650}{500}\right] \times 100 = 1.3 \times 100 = 130\%$