Question

(03.08 mc)
asher is able to sell his cell phone on two different websites, a and b. in the table, the different rates are represented by the functions a(t) and b(t), where t is time in months.

in what month will the price of his phone be less with website b than website a? (1 point)
5
6
7
8

Explanation:

Step1: Calculate \(A(t)\) and \(B(t)\) for \(t = 5\)

For \(A(t)=50(0.85)^{t}\), when \(t = 5\), \(A(5)=50\times(0.85)^{5}=50\times0.4437053125 = 22.185265625\)
For \(B(t)=50 - 5t\), when \(t = 5\), \(B(5)=50-5\times5=50 - 25=25\). Since \(B(5)>A(5)\)

Step2: Calculate \(A(t)\) and \(B(t)\) for \(t = 6\)

For \(A(t)=50(0.85)^{t}\), when \(t = 6\), \(A(6)=50\times(0.85)^{6}=50\times0.377149515625=18.85747578125\)
For \(B(t)=50 - 5t\), when \(t = 6\), \(B(6)=50-5\times6=50 - 30 = 20\). Since \(B(6)>A(6)\)

Step3: Calculate \(A(t)\) and \(B(t)\) for \(t = 7\)

For \(A(t)=50(0.85)^{t}\), when \(t = 7\), \(A(7)=50\times(0.85)^{7}=50\times0.31957708828125 = 15.9788544140625\)
For \(B(t)=50 - 5t\), when \(t = 7\), \(B(7)=50-5\times7=50 - 35=15\). Since \(B(7)<A(7)\)

Step4: Calculate \(A(t)\) and \(B(t)\) for \(t = 8\)

For \(A(t)=50(0.85)^{t}\), when \(t = 8\), \(A(8)=50\times(0.85)^{8}=50\times0.2716405250390625 = 13.582026251953125\)
For \(B(t)=50 - 5t\), when \(t = 8\), \(B(8)=50-5\times8=50 - 40 = 10\). But we already found the month when \(B(t)<A(t)\) at \(t = 7\)

Answer:

7