N=500(2.3)^((t)/( 12)) 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? (Ignore the % symbol when entering your answer. For example, if the answer is 11.2%, enter 11.2 .)

Question

N=500(2.3)^((t)/( 12)) 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? (Ignore the  % symbol when entering your answer. For example, if the answer is  11.2%, enter 11.2 .)

Bytelearn · Accepted Answer

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)^(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)^(12/12) = 500(2.3)^1Calculate N after 1 year: Calculate the value of N after one year. N = 500 * 2.3 = 1150Initial 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 = [(Final Value - Initial Value) / Initial Value] * 100. Percent Growth = [(1150 - 500) / 500] * 100Evaluate Percent Growth: Evaluate the percent growth. Percent Growth = [(650) / 500] * 100 = 1.3 * 100 = 130%

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