Algebra, STD2 EQ-Bank 7 MC

The relationship between variables \(x\) and \(y\) is \(y=k a^x\) where \(k>0, a>1\) and \(x\) is measured in days.

The value of \(y\) doubles every week.

Which of the following is closest to the value of \(a\) ?

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\(A\)

Show Worked Solution

\(\text{When}\ \ x=0, \ y=k\)

\(\text{1 week later, when}\ \ x=7:\)

\(\text{Option A:}\ \ y=k \times 1.1^{7}=1.948…\ \text{(almost double)}\)

\(\text{Option B:}\ \ y=k \times 1.14^{7}=10.54…\)

\(\text{Options C and D:}\ \ y \gt 10.54…\)

\(\Rightarrow A\)