(Solved): The following bar graph shows u.5. math SAT scores as a function of household incame. These data ca ...

The following bar graph shows u.5. math SAT scores as a function of household incame. These data can be modeled by \[ 5(x)+573-13 e^{-0.21 a 1 x} \] where \( S(x) \) is the averose math Sat seore of students whose housthold income a o Boursnd foltan ser vtar. Caleulate \( \lim _{x \rightarrow+\infty} S(x) \). (II an anwwer does thet exist. enter bote.) Lnterpret the answer, Students ahose parents earn an exceptionally larpe income scoce an averape of WANEFMAC? 10.3.C98. The following models approximate the pepularify of Facebock and routube among sociak media sits betweten two year. Facetook: \( F(t)=-6 t^{2}+15 t+17 \) percertape points YouTube: \( Y(t)=-g^{2}+6 .(t-1.4 \) percentage points (t is the number of years since the first year.) Caloulate \( \lim _{f \rightarrow+\infty} f(t) \) algebraicaly. \( \{1 f \) an answer does not exist, erber ONE.\} Interpret your anseer. In the lang term, the sopularity of facebook ameng social media shes will thcrease whout bound. In the tong term, the popularty of focebock among social media sien will staskils at this value. Calculate \( \operatorname{Imm}_{t \rightarrow+\infty} \frac{\text { Fit] }}{\text { rit }} \) algebraicathy. (\$f an anvwer does nat trist, enter DNE.) Interpret your answer. In the long term. Faceboek will be as booular as Yosfube. In the long term, Facebook will be more popular than voutube. In the long term, facebosk will be less popular than vostube. Comment on the results. frtrapolaing the models to obtain long-term predictions gives meaningful reswit. Evtrapolaning the modely to obtain long-term geedictions gives meaningless resiats. The percentage \( p(t) \) of children who can speak in at least single words by the age of \( t \) months can be approximated by the following equation. \[ p(t)=100\left(1-\frac{14,200}{t^{4,45}}\right) \quad(t \geq 8.5) \] Calculate \( \lim _{t \rightarrow+\infty} p(t) \cdot \) (If an answer does not exist, enter DNE.) \[ \lim _{t \rightarrow+\infty} p(t)= \] Interpret the results. The percentage of children who learn to speak approaches \( \quad \% \) as their age increases. The percentage \( q(t) \) of children who can speak in sentences of five or more words by the age of \( t \) months can be approximated by the following equation. \[ q(t)=100\left(1-\frac{5.27 \times 10^{17}}{t^{16}}\right)(t \geq 30) \] WANEFMAC7 10.3.100. The percentage \( \rho(t) \) of children who can speak in at least single words by the age of \( t \) months can be approximated by the following equation. \[ p(t)=100\left(1-\frac{12,300}{t^{4.45}}\right)(t \geq 8.5) \] Calculate \( \lim _{t \rightarrow+\infty}[p(t)-q(t)] \). (If an answer does not exist, enter DNE.) Interpret the result. Children who learn to speak in single words have a harder time learning to speak in sentences of five or more words. All children who learn to speak in single words eventually go on to learn to speak in sentences of five or more words. Children who learn to speak in single words have an easier time learning to speak in sentences of five or more words.