QuestionFind when two tree species will be the same height given their current heights and growth rates:
Tree A: 38 in, 4 in/yr; Tree B: 45.5 in, 25 in/yr.

Studdy Solution

STEP 1

Assumptions1. Tree A has a current height of38 inches and grows at an average rate of4 inches per year. . Tree B has a current height of45.5 inches and grows at an average rate of25 inches per year.
3. We are looking for the time it will take for the two trees to be the same height.

STEP 2

We can set up an equation to represent the heights of the two trees as a function of time. Let's denote the time in years as $t$ .
For tree A, the height at time $t$ is its current height plus its growth rate times $t$ .
$Height_A(t) =38 +4t$ For tree B, the height at time $t$ is its current height plus its growth rate times $t$ .
$Height_B(t) =45.5 +25t$

STEP 3

We want to find the time $t$ when the two trees are the same height. So, we set the two height functions equal to each other and solve for $t$ .
$38 +t =45.5 +25t$

STEP 4

To isolate $t$ , we can first subtract $4t$ from both sides of the equation.
$38 =45. +25t -4t$

STEP 5

implify the right side of the equation.
$38 =45.5 +21t$

STEP 6

Next, subtract $45.5$ from both sides of the equation to isolate $t$ .
$38 -45.5 =21t$

STEP 7

implify the left side of the equation.
$-7.5 =21t$

STEP 8

Finally, divide both sides of the equation by $21$ to solve for $t$ .
$t = -7.5 /21$

STEP 9

Calculate the value of $t$ .
$t = -7.5 /21 = -.357$ However, time cannot be negative. There seems to be a mistake in the problem or the data provided, as the slower-growing tree (A) is shorter than the faster-growing tree (B). Therefore, they will never be the same height. The solution is undefined.

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QuestionFind when two tree species will be the same height given their current heights and growth rates:
Tree A: 38 in, 4 in/yr; Tree B: 45.5 in, 25 in/yr.

Studdy Solution

STEP 1

Assumptions1. Tree A has a current height of38 inches and grows at an average rate of4 inches per year. . Tree B has a current height of45.5 inches and grows at an average rate of25 inches per year.
3. We are looking for the time it will take for the two trees to be the same height.

STEP 2

STEP 3

We want to find the time $t$ when the two trees are the same height. So, we set the two height functions equal to each other and solve for $t$ .
$38 +t =45.5 +25t$

STEP 4

To isolate $t$ , we can first subtract $4t$ from both sides of the equation.
$38 =45. +25t -4t$

STEP 5

implify the right side of the equation.
$38 =45.5 +21t$

STEP 6

Next, subtract $45.5$ from both sides of the equation to isolate $t$ .
$38 -45.5 =21t$

STEP 7

implify the left side of the equation.
$-7.5 =21t$

STEP 8

Finally, divide both sides of the equation by $21$ to solve for $t$ .
$t = -7.5 /21$

STEP 9

Calculate the value of $t$ .
$t = -7.5 /21 = -.357$ However, time cannot be negative. There seems to be a mistake in the problem or the data provided, as the slower-growing tree (A) is shorter than the faster-growing tree (B). Therefore, they will never be the same height. The solution is undefined.

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QuestionFind when two tree species will be the same height given their current heights and growth rates: Tree A: 38 in, 4 in/yr; Tree B: 45.5 in, 25 in/yr.

Studdy Solution

STEP 1

Assumptions1. Tree A has a current height of38 inches and grows at an average rate of4 inches per year. . Tree B has a current height of45.5 inches and grows at an average rate of25 inches per year.3. We are looking for the time it will take for the two trees to be the same height.

STEP 2

STEP 3

We want to find the time ttt when the two trees are the same height. So, we set the two height functions equal to each other and solve for ttt.38+t=45.5+25t38 +t =45.5 +25t38+t=45.5+25t

STEP 4

To isolate ttt, we can first subtract 4t4t4t from both sides of the equation.38=45.+25t−4t38 =45. +25t -4t38=45.+25t−4t

STEP 5

implify the right side of the equation.38=45.5+21t38 =45.5 +21t38=45.5+21t

STEP 6

Next, subtract 45.545.545.5 from both sides of the equation to isolate ttt.38−45.5=21t38 -45.5 =21t38−45.5=21t

STEP 7

implify the left side of the equation.−7.5=21t-7.5 =21t−7.5=21t

STEP 8

Finally, divide both sides of the equation by 212121 to solve for ttt.t=−7.5/21t = -7.5 /21t=−7.5/21

STEP 9

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QuestionFind when two tree species will be the same height given their current heights and growth rates:
Tree A: 38 in, 4 in/yr; Tree B: 45.5 in, 25 in/yr.

Assumptions1. Tree A has a current height of38 inches and grows at an average rate of4 inches per year. . Tree B has a current height of45.5 inches and grows at an average rate of25 inches per year.
3. We are looking for the time it will take for the two trees to be the same height.

We want to find the time $t$ when the two trees are the same height. So, we set the two height functions equal to each other and solve for $t$ .
$38 +t =45.5 +25t$

To isolate $t$ , we can first subtract $4t$ from both sides of the equation.
$38 =45. +25t -4t$

implify the right side of the equation.
$38 =45.5 +21t$

Next, subtract $45.5$ from both sides of the equation to isolate $t$ .
$38 -45.5 =21t$

implify the left side of the equation.
$-7.5 =21t$

Finally, divide both sides of the equation by $21$ to solve for $t$ .
$t = -7.5 /21$