Laurent invested some money in a bank account. The relationship between the elapsed time, t, in decades, since Laurent invested the money, and the total amount of money in the account, M_("decade ")(t), in dollars, is modeled by the following function: M_("decade ")(t)=4900*(1.5)^(t) Complete the following sentence about the yearly rate of change in the amount of money in the account. Round your answer to two decimal places. Every year, the amount of money in the account increases by a factor of

Question

Laurent invested some money in a bank account. The relationship between the elapsed time,  t, in decades, since Laurent invested the money, and the total amount of money in the account,  M_("decade ")(t), in dollars, is modeled by the following function:  M_("decade ")(t)=4900*(1.5)^(t) Complete the following sentence about the yearly rate of change in the amount of money in the account. Round your answer to two decimal places. Every year, the amount of money in the account increases by a factor of

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Convert growth factor: The given function for the total amount of money in the account is M_(＂decade ＂)(t) = 4900 * (1.5)^(t), where t is the time in decades. To find the yearly rate of change, we need to convert the growth factor from a per-decade basis to a per-year basis.Calculate tenth root: Since there are 10 years in a decade, we need to take the tenth root of the growth factor to find the yearly growth factor. The tenth root of 1.5 is calculated as (1.5)^(1/10).Find approximate value: Using a calculator, we find the tenth root of 1.5 to be approximately (1.5)^(1/10) ≈ 1.0414.Round to two decimal: Rounding the yearly growth factor to two decimal places gives us approximately 1.04.Determine yearly increase: Therefore, every year, the amount of money in the account increases by a factor of approximately 1.04.

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