Exponential Equations Introduction,Examples with Step-by-Step Explanations

The problems about Exponential Equations

Topic	Problem	Solution
None	An SUV is purchased new for $$ 31, 500$ . (b) Sup…	The initial value of the SUV is given as $V_{0} = $ 31, 500$ .
None	A bacteria culture initially contains 1500 bacter…	This problem involves exponential growth, which can be represented by the formula \(P = P0 * e^{rt}…
None	Find the solution of the exponential equation \[ …	Divide both sides of the equation by 100 to get ${1.05}^{2 t} = 5000$
None	Write the equation in exponential form. Assume th…	Write the equation in exponential form. Assume that all constants are positive and not equal to 1 .
None	A vehicle purchased for $$ 29, 800$ depreciates a…	The problem provides that a vehicle was purchased for $29,800 and depreciates at a constant rate of…
None	Solve the following equation for $x$ : \[ 2^{-x}=…	We are given the equation $2^{- x} = 15$ .
None	Solve for $y$ in the equation below. Round your a…	Take the natural logarithm (ln) of both sides of the equation $e^{y - 3} = 4$ . This gives us \(y-3 = …
None	Solve the equation. $2^{5 x + 1} = 4$ The solutio…	The given equation is an exponential equation. To solve it, we need to express both sides of the eq…
None	Solve the exponential equation. Express irrationa…	Take the natural logarithm on both sides of the equation $e^{x^{2}} = 128$ to bring down the expone…
None	Find a formula for the exponential function passi…	The general form of an exponential function is $f (x) = a b^{x}$ . We can use the two given points to …
None	The exponential model $A = 106.1 e^{0.02 t}$ descri…	The exponential model $A = 106.1 e^{0.02 t}$ describes the population, $A$ , of a country in milli…
None	The price $p$ , in dollars, of a specific car that…	Given the function $p (x) = 22, 265 (0.89)^{x}$ , where $p$ is the price of the car in dollars and \(…
None	Solve the given exponential equation. Express the…	Divide both sides of the equation by 3 to isolate the exponential term: $e^{x} = \frac{131}{3}$
None	Question 14 (3 points) Han purchased a car for $\…	The depreciation of the car can be modeled using an exponential decay formula. The general formula …
None	Solve the following exponential equation. Express…	Take the natural logarithm on both sides of the equation to bring down the exponent and solve for x…
None	Use a calculator with a $y^{x}$ key or a…	The exponential function $f (x) = 540 (1.032)^{x}$ models the population of a country, $f (x)$ , in m…
None	$a^{x} + b^{y} = c^{z}$	Given the equation: $a^{x} + b^{y} = c^{z}$
None	$2^{2 x} + 4 \cdot 2^{x} = - 4$	Let $y = 2^{x}$ , then the equation becomes $y^{2} + 4 y = - 4$
None	Work out the value of $k$ if \[ k \times 3^{-2}=4…	Rewrite the equation as: $k = \frac{4}{3^{- 2}}$
None	Solve the exponential equation for $x$ . \[ 9^…	9^{3x-10}=(81^{-1})^{\frac{1}{6}}
None	$7^{3 x - 6} + 100 = 101$	$7^{3 x - 6} = 1$
None	\( \begin{array}{l}5^{x}+5^{x}+5^{x}+5^{x}+5^{x}=…	$5^{x} + 5^{x} + 5^{x} + 5^{x} + 5^{x} = 5^{x + 1}$
None	6. Since 1992, the value of homes in a neighborho…	a. Since 2000 is 8 years after 1992, divide 16 years by 2 to get the half-growth period: \(\frac{16…
None	\( x^{3} \cdot x^{\stackrel{2}{?}}=\frac{1}{x^{12…	$x^{3} \cdot x^{y} = x^{3 + y}$