Question

Part A.1. Branch A is a linear function; Branch B is an exponential function2. Branch A is an exponential function; Branch B is a linear equation3. Both Branch A and Branch B are linear functions4.Both Branch A and Branch B are both exponential functionsPart B.Explain your response to Part A. Be sure to include an explanation for both Branch A and Branch B

Answer 1

Part A)

As for branch A, notice the following pattern

$\begin{gathered} 20=10\cdot2 \\ 40=10\cdot4=10\cdot2^2 \\ 80=10\cdot8=10\cdot2^3 \\ 160=10\cdot16=10\cdot2^4 \end{gathered}$

Therefore, the equation that models branch A is

$10\cdot2^n\to\text{ exponential function}$

Whereas, as for branch B

$\begin{gathered} 20 \\ 24=20+4 \\ 28=20+8=20+2\cdot4 \\ 32=20+12=20+3\cdot4 \\ \Rightarrow20+4n \end{gathered}$

which is a linear equation.

Thus, the answer to part A is

Branch A is an exponential function; Branch B is a linear equation, option 2.