Question

a company sells dahlias, the national flower of mexico. as the local growing season ends, the cost of each flower increases. the company determines the cost of each dahlia every month through winter and spring according to the expression 1.44^{\frac{x}{2}}, where x represents the number of months after october. which expression can also be used to determine the cost of each dahlia x months after october? 1.2^{x} 2.88^{x} 0.72^{x} 2.1^{x}

Explanation:

Step1: Use exponent - power rule

We know that \(a^{mn}=(a^{m})^{n}\). Here \(1.44^{\frac{x}{2}}=(1.44^{\frac{1}{2}})^{x}\).

Step2: Calculate the square - root of 1.44

Since \(1.2\times1.2 = 1.44\), then \(1.44^{\frac{1}{2}}=\sqrt{1.44}=1.2\). So \(1.44^{\frac{x}{2}}=(1.44^{\frac{1}{2}})^{x}=1.2^{x}\).

Answer:

\(1.2^{x}\)