suppose the number of hotdogs (in the millions) from 2017 to 2030 can be modeled by the following function…

suppose the number of hotdogs (in the millions) from 2017 to 2030 can be modeled by the following function: $f(t)=37.6e^{0.13t}$. approximate how many million (rounded to the nearest million) hotdogs were sold in 2023. then, approximate the year when the number of hotdogs reaches 64 million. remember, you are selecting two answers for this problem. 52 million 4 82 million -4 796 million 2021 29.328 million 2026

suppose the number of hotdogs (in the millions) from 2017 to 2030 can be modeled by the following function: $f(t)=37.6e^{0.13t}$. approximate how many million (rounded to the nearest million) hotdogs were sold in 2023. then, approximate the year when the number of hotdogs reaches 64 million. remember, you are selecting two answers for this problem. 52 million 4 82 million -4 796 million 2021 29.328 million 2026

Answer

Explanation:

Step1: Calculate hot - dogs sold in 2023

Find (t) for 2023. Since (t = 0) represents 2017, for 2023, (t=2023 - 2017=6). Substitute (t = 6) into (f(t)=37.6e^{0.13t}). [f(6)=37.6e^{0.13\times6}=37.6e^{0.78}] [e^{0.78}\approx2.1814] [f(6)=37.6\times2.1814\approx82.02\approx82] (rounded to the nearest million)

Step2: Find the year when (f(t)=64)

Set (f(t)=64), so (64 = 37.6e^{0.13t}). First, divide both sides by 37.6: (\frac{64}{37.6}=e^{0.13t}), (\frac{64}{37.6}\approx1.7021 = e^{0.13t}). Take the natural - logarithm of both sides: (\ln(1.7021)=0.13t). Since (\ln(1.7021)\approx0.532), then (t=\frac{\ln(1.7021)}{0.13}=\frac{0.532}{0.13}\approx4.09). Since (t = 0) is 2017, the year is (2017 + 4=2021).

Answer:

82 million 2021