Problemas
Given the following exponential function, identify whether th represents growth or decay,and determine the percentage rat increase or decrease. y=4300(0.042)^x Answer Attempt 1 out of 2 square square % increase
Solución
Karinaprofessionell · Tutor durante 6 años
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The function represents decay, with a percentage decrease of 95.8%.
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## Step 1<br />The given function is \(y=4300(0.042)^{x}\). This is an exponential function, which is generally represented in the form \(y=ab^{x}\), where \(a\) is the initial amount, \(b\) is the growth factor, and \(x\) is the time.<br /><br />## Step 2<br />In this function, the base of the exponent, \(b\), is 0.042. Since this value is less than 1, it indicates that the function represents decay, not growth.<br /><br />## Step 3<br />To find the percentage rate of decrease, we subtract the base from 1 and multiply by 100. This gives us the percentage decrease.<br /><br />### **Formula**: <br />The formula to calculate the percentage decrease is \((1 - b) \times 100\).<br /><br />## Step 4<br />Substitute the value of \(b\) into the formula.<br /><br />### **Calculation**: <br />\((1 - 0.042) \times 100 = 95.8\%\).
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