Solving Exponential Equations
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- Exponential Functions India is the second most populous country in the world with a population in 2008 of about 1.14 billion people. The population is growing by about 1.34% eac…
By Precalculus: An Investigation of Functions
- Difference between Exponential and Linear growth To see more clearly the difference between exponential and linear growth, compare the two tables and graphs below, which illustr…
By Precalculus: An Investigation of Functions
- Finding Equations of Exponential Function In the previous examples, we were able to write equations for exponential functions since we knew the initial quantity and the growth r…
By Precalculus: An Investigation of Functions
- Compound Interest In the bank certificate of deposit (CD) example earlier in the section, we encountered compound interest. typically bank accounts and other savings instruments…
By Precalculus: An Investigation of Functions
- Because of compounding throughout the year, with compound interest the actual increase in a year is more than the annual percentage rate. If 1,00\1,001,00 were invested at 10%, …
By Precalculus: An Investigation of Functions
- A Limit to Compounding As we saw earlier, the amount we earn increases as we increase the compounding frequency. The table, though, shows that the increase from annual to semi-a…
By Precalculus: An Investigation of Functions
- Graphs of Exponential Functions Like with linear functions, the graph of an exponential function is determined by the values for the parameters in the function's formula. To get…
By Precalculus: An Investigation of Functions, Alex Federspiel
- Transformations of Exponential Graphs While exponential functions can be transformed following the same rules as any function, there are a few interesting features of transforma…
By Precalculus: An Investigation of Functions, Alex Federspiel
Problems 37
- Solve for xxx. e2x+6=10.e^{2x}+6=10.e2x+6=10.
- Solve for xxx. ex−12=24e^{\frac{x-1}{2}}=24e2x−1=24
- Solve for xxx, rounding to the nearest hundredth. 164x=28616^{4x}=286164x=286
- Solve for xxx to the nearest tenth. 16x−5=4916^{x-5}=4916x−5=49
- Solve for xxx to the nearest tenth. 137x−11=7113^{7x-11}=71137x−11=71
- List all values of xxx satisfying 22x+8=9⋅2x2^{2x} + 8 = 9 \cdot 2^x22x+8=9⋅2x.
- Solve the equation 22x−7⋅2x−8=02^{2x} - 7 \cdot 2^x - 8 = 022x−7⋅2x−8=0.
- Solve 32x=832^x = 832x=8.
- Solve the equation 5x−5x−1=1005^x - 5^{x-1} = 1005x−5x−1=100.
- Solve for xxx. ex−5⋅ex−1=e−4e^{x-5} \cdot e^{x-1} = e^{-4}ex−5⋅ex−1=e−4
- Solve for xxx. 72x+5=73x−47^{2x + 5} = 7^{3x - 4}72x+5=73x−4
- Solve for xxx. 3⋅24x−1=48⋅22x+33 \cdot 2^{4x - 1} = 48 \cdot 2^{2x + 3}3⋅24x−1=48⋅22x+3
- For the table above, could the table represent a function that is linear, exponential, or neither?
- For the table above, could the table represent a function that is linear, exponential, or neither?
- For the table above, could the table represent a function that is linear, exponential, or neither?
- For the table above, could the table represent a function that is linear, exponential, or neither?
- For the table above, could the table represent a function that is linear, exponential, or neither?
- For the table above, could the table represent a function that is linear, exponential, or neither?
- A population numbers 11,000 organisms initially and grows by 8.5% each year. Write an exponential model for the population.
- A population numbers 6,000 organisms initially and grows by 1.2% each day. Write an exponential model for the population.
- The fox population in a certain region has an annual growth rate of 9 percent per year. It is estimated that the population in the year 2010 was 23,900. Estimate the fox populat…
- The amount of area covered by blackberry bushes in a park has been growing by 12% each year. It is estimated that the area covered in 2009 was 4,500 square feet. Estimate the ar…
- A vehicle purchased for 32,500 depreciates at a constant rate of 5% each year. Determine the approximate value of the vehicle 12 years after purchase.
- Find aaa and bbb for an exponential function of the form y=abxy=ab^xy=abx passing through the two points. (0,6),(3,750)(0,6),(3,750)(0,6),(3,750)
- Find aaa and bbb for an exponential function of the form y=abxy=ab^xy=abx passing through the two points. (0,3),(2,75)(0,3),(2,75)(0,3),(2,75)
- Find aaa and bbb for an exponential function of the form y=abxy=ab^xy=abx passing through the two points. (0,2000),(2,20)(0,2000),(2,20)(0,2000),(2,20)
- Find aaa and bbb for an exponential function of the form y=abxy=ab^xy=abx passing through the two points. (0,9000),(3,72)(0,9000),(3,72)(0,9000),(3,72)
- Find aaa and bbb for an exponential function of the form y=abxy=ab^xy=abx passing through the two points. (−1,32),(3,24)\begin{pmatrix}-1,\dfrac32\end{pmatrix},(3,24)(−1,23),(…
- Find aaa and bbb for an exponential function of the form y=abxy=ab^xy=abx passing through the two points. (−1,25),(1,10)\begin{pmatrix}-1,\dfrac25\end{pmatrix},(1,10)(−1,52),(…
- Find aaa and bbb for an exponential function of the form y=abxy=ab^xy=abx passing through the two points. (−2,6),(3,1)(-2,6),(3,1)(−2,6),(3,1)
- A radioactive substance decays exponentially. A scientist begins with 100 milligrams of a radioactive substance. After 35 hours, 50 mg of the substance remains. How many milligr…
- A house was valued at 110,000\110,000110,000 in the year 198519851985. The value appreciated to 145,000\145,000145,000 by the year 200520052005. What was the annual growth rate …
- A house was valued at 110,000\110,000110,000 in the year 198519851985. The value appreciated to 145,000\145,000145,000 by the year 200520052005. The annual growth rate is 1.39%.…
- An investment was valued at 38,000\38,00038,000 in the year 1995. The value appreciated to 14,000\14,00014,000 by the year 2008. What was the annual growth rate between 1995 and…
- A car was valued at 38,000\38,00038,000 in the year 2003. The value depreciated to 11,000\11,00011,000 by the year 2009. Assume that the car value continues to drop by the same …
- Suppose Sudan finds his soulmate on Tinder. She loves long walks in the meadows, and other rhino activities. Furthermore, assume a rhino only gives birth once a year. How many y…
- Suppose aaa and bbb are real numbers such that 2a=3b=62^a = 3^b = 62a=3b=6. Which of the following relations is satisfied by aaa and bbb?