A manufacturing plant earned $80 per man-hour of labor when it opened. Each year, the plant earns an additional 5% per man-hour. Write a function that gives the amount A(t) that the plant earns per man-hour t years after it opens. A(t)=

Identify initial amount and increase rate: Identify the initial amount earned per man-hour and the annual increase rate. The initial amount earned per man-hour is $80. The annual increase rate is 5% or 0.05 in decimal form.Write function for amount earned per man-hour: Write the function for the amount earned per man-hour after t years. The amount earned per man-hour after t years can be represented by an exponential growth function because the earnings increase by a constant percentage each year. The general form of an exponential growth function is A(t) = A_0 * (1 + r)^t, where A_0 is the initial amount, r is the growth rate, and t is the time in years.Substitute values into exponential growth function: Substitute the given values into the exponential growth function. Using the initial amount A_0 = $80 and the growth rate r = 0.05, we get the function A(t) = 80 * (1 + 0.05)^t.Simplify the function: Simplify the function. The function simplifies to A(t) = 80 * (1.05)^t. This function represents the amount the plant earns per man-hour t years after it opens.

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A manufacturing plant earned
$80 per man-hour of labor when it opened. Each year, the plant earns an additional
5% per man-hour.
Write a function that gives the amount
A(t) that the plant earns per man-hour
t years after it opens.

A(t)=

A manufacturing plant earned $\$ 80$ per man-hour of labor when it opened. Each year, the plant earns an additional $5 \%$ per man-hour. $\newline$ Write a function that gives the amount $A(t)$ that the plant earns per man-hour $t$ years after it opens. $\newline$ $A(t)=$

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Math Problems

Algebra 1

Write exponential functions: word problems

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Q. A manufacturing plant earned

\$ 80

per man-hour of labor when it opened. Each year, the plant earns an additional

5 \%

per man-hour.

\newline

Write a function that gives the amount

A(t)

that the plant earns per man-hour

t

years after it opens.

\newline

A(t)=

Identify initial amount and increase rate: Identify the initial amount earned per man-hour and the annual increase rate. $\newline$ The initial amount earned per man-hour is $\$80$ . The annual increase rate is $5\%$ or $0.05$ in decimal form.
Write function for amount earned per man-hour: Write the function for the amount earned per man-hour after $t$ years. $\newline$ The amount earned per man-hour after $t$ years can be represented by an exponential growth function because the earnings increase by a constant percentage each year. $\newline$ The general form of an exponential growth function is $A(t) = A_0 \times (1 + r)^t$ , where $A_0$ is the initial amount, $r$ is the growth rate, and $t$ is the time in years.
Substitute values into exponential growth function: Substitute the given values into the exponential growth function. $\newline$ Using the initial amount $A_0 = \$80$ and the growth rate $r = 0.05$ , we get the function $A(t) = 80 \times (1 + 0.05)^t$ .
Simplify the function: Simplify the function. $\newline$ The function simplifies to $A(t) = 80 \times (1.05)^t$ . This function represents the amount the plant earns per man-hour $t$ years after it opens.