Question

(1 point)
according to data collected by the world bank, the number of internet users in the united states and china has varied over the past decade as follows:
a) find a linear regression modeling the number (in millions) of internet users u in the united states t years from 1998. round your slope and vertical intercept to three decimal places.
the number of internet users in the united states t years from 1998 is u(t) = 19.141t + 48.208

b) find a linear regression modeling the number (in millions) of internet users c in china t years from 1998. round your slope and vertical intercept to three decimal places.
the number of internet users in china t years from 1998 is c(t) = 21.170t - 16.548

c) according to your models when will china have more internet users than the united states? round to the nearest year.
after the year 2030, china will have more internet users.

Explanation:

Step1: Set up the inequality

We want to find when $C(t)>U(t)$. Given $U(t)=19.141t + 48.208$ and $C(t)=21.170t-16.548$, we set up the inequality $21.170t - 16.548>19.141t + 48.208$.

Step2: Rearrange the inequality

Subtract $19.141t$ from both sides: $(21.170t-19.141t)-16.548>19.141t - 19.141t+ 48.208$, which simplifies to $2.029t-16.548>48.208$.

Step3: Isolate the variable

Add $16.548$ to both sides: $2.029t-16.548 + 16.548>48.208+16.548$, getting $2.029t>64.756$. Then divide both sides by $2.029$: $t>\frac{64.756}{2.029}$.

Step4: Calculate the value of t

$\frac{64.756}{2.029}\approx31.915$. Since $t$ represents the number of years from 1998, the year is $1998 + 32=2030$.

Answer:

2030