the worldwide number (in millions) of a particular phone sold can be approximated by the function f(x)=…

the worldwide number (in millions) of a particular phone sold can be approximated by the function f(x)= - 874 + 401 in x, where x = 11 corresponds to 2011. (a) what was the number of worldwide sales for the particular phone in 2015? (b) if the model continues to be accurate, what was the first full year in which the particular phone sales exceed 274 million? (a) to find the number of worldwide sales in 2015, substitute for x in the function. (simplify your answer.)

the worldwide number (in millions) of a particular phone sold can be approximated by the function f(x)= - 874 + 401 in x, where x = 11 corresponds to 2011. (a) what was the number of worldwide sales for the particular phone in 2015? (b) if the model continues to be accurate, what was the first full year in which the particular phone sales exceed 274 million? (a) to find the number of worldwide sales in 2015, substitute for x in the function. (simplify your answer.)

Answer

Explanation:

Step1: Determine the value of x for 2015

Since x = 11 corresponds to 2011, for 2015, x=11+(2015 - 2011)=15.

Step2: Calculate the sales in 2015

Substitute x = 15 into the function f(x)=- 874+401lnx. f(15)=-874 + 401ln(15) First, find ln(15)≈2.7081. Then, 401×2.7081 = 1086.9481. f(15)=-874+1086.9481 = 212.9481.

Step3: Solve for the year when sales exceed 274 million

Set f(x)>274, so - 874+401lnx>274. Add 874 to both sides: 401lnx>274 + 874=1148. Then, lnx > \frac{1148}{401}\approx2.8628. Exponentiate both sides using the base - e: x>e^{2.8628}. Since e^{2.8628}\approx17.57. Since x represents the year - related value and it must be an integer, x = 18. The year is 2011+(18 - 11)=2018.

Answer:

(a) Substitute 15 for x in the function. The number of worldwide sales in 2015 is approximately 212.95 million. (b) The first full - year in which the particular phone sales exceed 274 million is 2018.