Two solutions were found :<span> t = 8 t = 0</span>
Reformatting the input :
Changes made to your input should not affect the solution:
(1): "t2" was replaced by "t^2".
Step by step solution :Skip Ad
<span>Step 1 :</span><span>Step 2 :</span>Pulling out like terms :
<span> 2.1 </span> Pull out like factors :
<span> t2 - 8t</span> = t • (t - 8)
<span>Equation at the end of step 2 :</span> t • (t - 8) = 0
<span>Step 3 :</span>Theory - Roots of a product :
<span> 3.1 </span> A product of several terms equals zero.<span>
</span>When a product of two or more terms equals zero, then at least one of the terms must be zero.<span>
</span>We shall now solve each term = 0 separately<span>
</span>In other words, we are going to solve as many equations as there are terms in the product<span>
</span>Any solution of term = 0 solves product = 0 as well.
Solving a Single Variable Equation :
<span> 3.2 </span> Solve : t = 0<span>
</span> Solution is t = 0
Solving a Single Variable Equation :
<span> 3.3 </span> Solve : t-8 = 0<span>
</span>Add 8 to both sides of the equation :<span>
</span> t = 8
Two solutions were found :<span> t = 8<span> t = 0</span></span>
Answer: 90
Step-by-step explanation:
To check the decay rate, we need to check the variation in y-axis.
Since our interval is
![-2We need to evaluate both function at those limits.At x = -2, we have a value of 4 for both of them, at x = 0 we have 1 for the exponential function and 0 to the quadratic function. Let's call the exponential f(x), and the quadratic g(x).[tex]\begin{gathered} f(-2)=g(-2)=4 \\ f(0)=1 \\ g(0)=0 \end{gathered}](https://tex.z-dn.net/?f=-2We%20need%20to%20evaluate%20both%20function%20at%20those%20limits.%3Cp%3E%3C%2Fp%3E%3Cp%3EAt%20x%20%3D%20-2%2C%20we%20have%20a%20value%20of%204%20for%20both%20of%20them%2C%20at%20x%20%3D%200%20we%20have%201%20for%20the%20exponential%20function%20and%200%20to%20the%20quadratic%20function.%20Let%27s%20call%20the%20exponential%20f%28x%29%2C%20and%20the%20quadratic%20g%28x%29.%3C%2Fp%3E%3Cp%3E%3C%2Fp%3E%5Btex%5D%5Cbegin%7Bgathered%7D%20f%28-2%29%3Dg%28-2%29%3D4%20%5C%5C%20f%280%29%3D1%20%5C%5C%20g%280%29%3D0%20%5Cend%7Bgathered%7D)
To compare the decay rates we need to check the variation on the y-axis of both functions.
Now, we calculate their ratio to find how they compare:
This tell us that the exponential function decays at three-fourths the rate of the quadratic function.
And this is the fourth option.
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