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Juan purchased an antique that had a value of \$200$200dollar sign, 200 at the time of purchase. Each year, the value of the antique is estimated to increase 10\%10%10, percent over its value the previous year. The estimated value of the antique, in dollars, 222 years after purchase can be represented by the expression 200a200a200, a, where aaa is a constant. What is the value of aaa ?

Respuesta :

Answer:

The value of a is [tex](\frac{11}{10} )^{222}[/tex].

Step-by-step explanation:

At the time of purchase, the value of the antique is $200.

After one year the value will increase 10%.

Hence, after one year, the value of the antique will be [tex]\frac{110}{100} \times200[/tex] = 220.

Similarly, after two year, the value will be [tex]200\times (\frac{110}{100} )^{2}[/tex].

Thus, 222 years after purchase, the value of the antique will be [tex]200\times (\frac{110}{100} )^{222} = 200\times (\frac{11}{10} )^{222}[/tex].

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