The following table shows the height at half-second intervals of a rock that breaks free from the top of a 390 -foot-tall cliff and falls without obstruction to the river below.
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Step 1 of 3 : The linear function of best fit that models the height of the rock after $t$ seconds is $h (t) = - 48 t + 410$ . What is the linear-model height of the rock at time $t = 0$ ? Round your answer to the nearest foot, if necessary.
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Final Answer: The linear-model height of the rock at time $t = 0$ is $410$ feet.

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Step 1 ：The question asks for the height of the rock at time $t = 0$ according to the linear model $h (t) = - 48 t + 410$ . To find this, we simply need to substitute $t = 0$ into the equation and solve for $h (t)$ .

Step 2 ：Substitute $t = 0$ into the equation: $h_{t} = 410$

Step 3 ：Final Answer: The linear-model height of the rock at time $t = 0$ is $410$ feet.

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