Questions: A baby that weighs 6 lb at birth may increase his weight by 12% per month. Use the function f(t)=K(1+r)^t, where K is the initial value, r is the decimal value of the percentage of increase (r=0.12) and t is the time in months. How much would the baby weigh in one month? Two months? Six months? Nine months? One year? Round your answers to the nearest tenth of a pound. Age Weight (lbs) one month two months six months nine months one year

A baby that weighs 6 lb at birth may increase his weight by 12% per month. Use the function f(t)=K(1+r)^t, where K is the initial value, r is the decimal value of the percentage of increase (r=0.12) and t is the time in months. How much would the baby weigh in one month? Two months? Six months? Nine months? One year? Round your answers to the nearest tenth of a pound. Age Weight (lbs) one month two months six months nine months one year
Transcript text: A baby that weighs 6 lb at birth may increase his weight by $12 \%$ per month. Use the function $f(t)=K(1+r)^{t}$, where $K$ is the initial value, $r$ is the decimal value of the percentage of increase $(r=0.12)$ and $t$ is the time in months. How much would the baby weigh in one month? Two months? Six months? Nine months? One year? Round your answers to the nearest tenth of a pound. \begin{tabular}{c|c} Age & Weight (lbs) \\ \hline one month & $\square$ \\ \hline two months & $\square$ \\ \hline six makiths & $\square$ \\ \hline nine months & $\square$ \\ \hline one year & $\square$ \end{tabular}
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Solution

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Solution Steps

Step 1: Identify the Parameters

The initial value (K) is given as 6, the rate of increase (r) as 0.12, and the time period (t) as 1 intervals.

Step 2: Substitute into the Exponential Growth Formula

The formula to calculate the future value is \(f(t) = K(1 + r)^t\). Substituting the given values into the formula gives us \(f(1) = 6(1 + 0.12)^1\).

Step 3: Calculate the Future Value

Calculating the future value gives us \(f(1) = 6.7\).

Final Answer: The future value after 1 time intervals is 6.7.

Step 1: Identify the Parameters

The initial value (K) is given as 6, the rate of increase (r) as 0.12, and the time period (t) as 2 intervals.

Step 2: Substitute into the Exponential Growth Formula

The formula to calculate the future value is \(f(t) = K(1 + r)^t\). Substituting the given values into the formula gives us \(f(2) = 6(1 + 0.12)^2\).

Step 3: Calculate the Future Value

Calculating the future value gives us \(f(2) = 7.5\).

Final Answer: The future value after 2 time intervals is 7.5.
Step 1: Identify the Parameters

The initial value (K) is given as 6, the rate of increase (r) as 0.12, and the time period (t) as 6 intervals.

Step 2: Substitute into the Exponential Growth Formula

The formula to calculate the future value is \(f(t) = K(1 + r)^t\). Substituting the given values into the formula gives us \(f(6) = 6(1 + 0.12)^6\).

Step 3: Calculate the Future Value

Calculating the future value gives us \(f(6) = 11.8\).

Final Answer: The future value after 6 time intervals is 11.8.
Step 1: Identify the Parameters

The initial value (K) is given as 6, the rate of increase (r) as 0.12, and the time period (t) as 9 intervals.

Step 2: Substitute into the Exponential Growth Formula

The formula to calculate the future value is \(f(t) = K(1 + r)^t\). Substituting the given values into the formula gives us \(f(9) = 6(1 + 0.12)^9\).

Step 3: Calculate the Future Value

Calculating the future value gives us \(f(9) = 16.6\).

Final Answer: The future value after 9 time intervals is 16.6.
Step 1: Identify the Parameters

The initial value (K) is given as 6, the rate of increase (r) as 0.12, and the time period (t) as 12 intervals.

Step 2: Substitute into the Exponential Growth Formula

The formula to calculate the future value is \(f(t) = K(1 + r)^t\). Substituting the given values into the formula gives us \(f(12) = 6(1 + 0.12)^12\).

Step 3: Calculate the Future Value

Calculating the future value gives us \(f(12) = 23.4\).

Final Answer: The future value after 12 time intervals is 23.4.
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