Chapter 4: Problem 16
Solve each exponential equation by expressing each side as a power of the same base and then equating exponents. $$7^{\frac{x-2}{6}}=\sqrt{7}$$
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Chapter 4: Problem 16
Solve each exponential equation by expressing each side as a power of the same base and then equating exponents. $$7^{\frac{x-2}{6}}=\sqrt{7}$$
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Use your graphing utility to graph each side of the equation in the same viewing rectangle. Then use the \(x\) -coordinate of the intersection point to find the equation's solution=set. Verify this value by direct substitution into the equation. $$2^{x+1}=8$$
Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. If 4000 dollar is deposited into an account paying 3% interest compounded annually and at the same time 2000 dollar is deposited into an account paying 5% interest compounded annually, after how long will the two accounts have the same balance? Round to the nearest year.
Check each proposed solution by direct substitution or with a graphing utility. $$(\log x)(2 \log x+1)=6$$
Use the exponential growth model, \(A=A_{0} e^{k t},\) to show that the time it takes a population to double (to grow from \(A_{0}\) to \(\left.2 A_{0}\right)\) is given by \(t=\frac{\ln 2}{k}\)
Complete the table for a savings account subject to \(n\) compoundings yearly \(\left[A=P\left(1+\frac{r}{n}\right)^{m}\right]\). Round answers to one decimal place. Amount Invested 7250 dollar Number of Compounding Periods 12 Annual Interest Rate 6.5% A ccumulated Amount 15,000 dollar Time \(t\) in Years ________
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