Resourcesdown chevron
Testimonials
Plans
Sign in
Sign up
Resourcesright arrow
Testimonials
Plans
Bytelearn - cat image with glassesAI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Equation of a Line : y=mx+b MTH 1W Section 4 Test: Modeling with Graphs (Modified) Slope =m=(" rise ")/(" run ")=(y_(2)-y_(1))/(x_(2)-x_(1)) Page 5 Optional Bonus Question [8 marks] 13. A pattern of toothpicks is shown. [2] (a) Complete the given table. [1] (b) Apply first difference calculation on the table. [1] (c) Is the pattern linear or non-linear? [2] (d) Write the equation for the relation. 1 house z of Houses Fof Toothpicks 1 2 3 4 [2] (e) Extrapolate the relation to predict the outcome for 10 houses.

Equation of a Line : y=mx+b y=m x+b \newlineMTH 11W\newlineSection 44 Test: Modeling with Graphs (Modified)\newlineSlope =m= rise  run =y2−y1x2−x1 =m=\frac{\text { rise }}{\text { run }}=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} \newlinePage 55\newlineOptional Bonus Question [88 marks]\newline1313. A pattern of toothpicks is shown.\newline[22] (a) Complete the given table.\newline[11] (b) Apply first difference calculation on the table.\newline[11] (c) Is the pattern linear or non-linear?\newline[22] (d) Write the equation for the relation.\newline11 house\newline\begin{tabular}{|c|c|}\newline\hline \begin{tabular}{c} \newlinez of \\\newlineHouses\newline\end{tabular} & \begin{tabular}{c} \newlineFof \\\newlineToothpicks\newline\end{tabular} \\\newline\hline 11 & \\\newline\hline 22 & \\\newline\hline 33 & \\\newline\hline 44 & \\\newline\hline\newline\end{tabular}\newline[22] (e) Extrapolate the relation to predict the outcome for 1010 houses.

View step-by-step helpView step-by-step help
Homeright chevron icon
Math Problemsright chevron icon
Algebra 1right chevron icon
Compare linear and exponential growthright chevron icon

Full solution

Q. Equation of a Line : y=mx+b y=m x+b \newlineMTH 11W\newlineSection 44 Test: Modeling with Graphs (Modified)\newlineSlope =m= rise  run =y2−y1x2−x1 =m=\frac{\text { rise }}{\text { run }}=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} \newlinePage 55\newlineOptional Bonus Question [88 marks]\newline1313. A pattern of toothpicks is shown.\newline[22] (a) Complete the given table.\newline[11] (b) Apply first difference calculation on the table.\newline[11] (c) Is the pattern linear or non-linear?\newline[22] (d) Write the equation for the relation.\newline11 house\newline\begin{tabular}{|c|c|}\newline\hline \begin{tabular}{c} \newlinez of \\\newlineHouses\newline\end{tabular} & \begin{tabular}{c} \newlineFof \\\newlineToothpicks\newline\end{tabular} \\\newline\hline 11 & \\\newline\hline 22 & \\\newline\hline 33 & \\\newline\hline 44 & \\\newline\hline\newline\end{tabular}\newline[22] (e) Extrapolate the relation to predict the outcome for 1010 houses.
  1. Identify Toothpick Count: (a) To complete the table, we need to count the number of toothpicks for each house. Let's assume the pattern is consistent and we can find it by looking at the first few houses.
  2. Calculate First Difference: (b) First difference calculation involves subtracting the number of toothpicks in the previous house from the current house to see if the difference is constant.
  3. Determine Linearity: (c) If the first difference is constant, the pattern is linear. If not, it's non-linear.
  4. Find Equation Parameters: (d) To write the equation for the relation, we need to identify the slope mm and yy-intercept bb from the pattern or the completed table.
  5. Extrapolate for 1010 Houses: (e) To extrapolate the relation for 1010 houses, we'll use the equation we found in step (d) and plug in x=10x=10.

More problems from Compare linear and exponential growth

Question
Jill bought a used motorcycle from a seller online for $1,200. The seller will charge her $5 a day to store the motorcycle at his house until she is able to pick it up. You can use a function to describe the total amount of money Jill will owe the seller if she waits xx days to pick up the motorcycle.\newlineWrite an equation for the function. If it is linear, write it in the form g(x)=mx+bg(x) = mx + b. If it is exponential, write it in the form g(x)=a(b)xg(x) = a(b)^x.\newlineg(x)=‾g(x) = \underline{\hspace{3em}}
Get tutor helpright-arrow

Posted 5 months ago

Question
How does f(t)=−2t−7f(t)=-2t-7 change over the interval from t=−7t=-7 to t=−6t=-6?\newlineChoices:\newline[f(t) decreases by 2]\left[\text{f(t) decreases by } 2\right]\newline[f(t) increases by 2]\left[\text{f(t) increases by } 2\right]\newline[f(t) increases by 200%]\left[\text{f(t) increases by } 200\%\right]\newline[f(t) decreases by a factor of 2]\left[\text{f(t) decreases by a factor of } 2\right]
Get tutor helpright-arrow

Posted 5 months ago

Question
How does g(t)=9tg(t)=9^t change over the interval from t=1t=1 to t=3t=3?\newlineChoices: \newline[g(t) decreases by a factor of 81]\left[\text{g(t) decreases by a factor of } 81\right]\newline[g(t) increases by a factor of 81]\left[\text{g(t) increases by a factor of } 81\right]\newline[g(t) increases by 18%]\left[\text{g(t) increases by } 18\%\right]\newline[g(t) decreases by 9%]\left[\text{g(t) decreases by } 9\%\right]
Get tutor helpright-arrow

Posted 5 months ago

Question
Both of these functions grow as xx gets larger and larger. Which function eventually exceeds the other?\newline Choices:\newline(A)f(x)=8x+3.3(A)f(x) = 8x + 3.3\newline(B)g(x)=3.3x−5(B)g(x) = 3.3^x - 5
Get tutor helpright-arrow

Posted 6 months ago

Question
Both of these functions grow as x x gets larger and larger. Which function eventually exceeds the other?\newlineChoices:\newline(A) f(x)=2x+9(A) \ f(x) = 2x + 9 \newline(B) g(x)=2x(B)\ g(x) = 2^x
Get tutor helpright-arrow

Posted 6 months ago

Question
The functions f(x) f(x) and g(x) g(x) are differentiable. \newlineThe function h(x) h(x) is defined as: h(x)=g(x)f(x) h(x)=\frac{g(x)}{f(x)} \newlineIf f(8)=1 f(8)=1 , f′(8)=−6 f'(8)=-6 , g(8)=8 g(8)=8 , and g′(8)=−10 g'(8)=-10 , what is h′(8) h'(8) ? \newlineSimplify any fractions. \newlineh′(8)= h'(8)= ______
Get tutor helpright-arrow

Posted 6 months ago

Question
The functions p(x) p(x) and q(x) q(x) are differentiable. \newlineThe function r(x) r(x) is defined as: r(x)=p(x)q(x) r(x)= \frac{p(x)}{q(x)} \newlineIf p(3)=2 p(3)= 2 , p′(3)=4 p'(3)= 4 , q(3)=6 q(3)= 6 , and q′(3)=9 q'(3)= 9 , what is r′(3) r'(3) ? \newlineSimplify any fractions. \newliner′(3)= r'(3)= _____
Get tutor helpright-arrow

Posted 7 months ago

Question
The functions u(x) u(x) and v(x) v(x) are differentiable. \newlineThe function w(x) w(x) is defined as: w(x)=u(x)v(x) w(x)= \frac{u(x)}{v(x)} \newlineIf u(5)=3 u(5)= 3 , u′(5)=−2 u'(5)= -2 , v(5)=7 v(5)= 7 , and v′(5)=1 v'(5)= 1 , what is w′(5) w'(5) ? \newlineSimplify any fractions. \newlinew′(5)= w'(5)= _____
Get tutor helpright-arrow

Posted 7 months ago

Question
The functions a(x) a(x) and b(x) b(x) are differentiable. \newlineThe function c(x) c(x) is defined as: c(x)=a(x)b(x) c(x)= \frac{a(x)}{b(x)} \newlineIf a(2)=4 a(2)= 4 , a′(2)=5 a'(2)= 5 , b(2)=1 b(2)= 1 , and b′(2)=−3 b'(2)= -3 , what is c′(2) c'(2) ? \newlineSimplify any fractions. \newlinec′(2)= c'(2)= _____
Get tutor helpright-arrow

Posted 7 months ago

Question
The functions m(x) m(x) and n(x) n(x) are differentiable. \newlineThe function o(x) o(x) is defined as: o(x)=m(x)n(x) o(x)= \frac{m(x)}{n(x)} \newlineIf m(7)=2 m(7)= 2 , m′(7)=−1 m'(7)= -1 , n(7)=4 n(7)= 4 , and n′(7)=8 n'(7)= 8 , what is o′(7) o'(7) ? \newlineSimplify any fractions. \newlineo′(7)= o'(7)= _____
Get tutor helpright-arrow

Posted 7 months ago

View all (427)

Related topics

Algebra - Order of OperationsAlgebra - Distributive Property`X` and `Y` AxesGeometry - Scalene TriangleCommon MultipleGeometry - Quadrant