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A certain country's consumer price index is approximated by a(t) = 100e0.024t, where t represents the number of years. use the function to determine the year in which costs will be 50% higher than in year 0.

Respuesta :

znk

Answer:

[tex]\boxed{\text{Year 17}}[/tex]

Step-by-step explanation:

[tex]a(t) = 100e^{0.024t}[/tex]

Data:

a(t) = 150

a(0) = 100

Calculations :

[tex]\begin{array}{rcll}150 & = & 100e^{0.024t} & \\\\1.50 & = & e^{0.024t} & \text{Divided each side by 100}\\0.4055 & = & 0.024t & \text{Took the ln of each side}\\t & \approx & \mathbf{17} & \text{Divided each side by 0.024}\\\end{array}[/tex]

[tex]\text{The consumer price index will be 50 \% higher in } \boxed{\textbf{year 17}}[/tex]

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