Resourcesdown chevron
Testimonials
Plans
Sign in
Sign up
Resourcesright arrow
Testimonials
Plans
Bytelearn - cat image with glassesAI tutor

Welcome to Bytelearn!

Let’s check out your problem:

What is the value of A when we rewrite ((2)/(3))^(x+4)-((2)/(3))^(x) as A*((2)/(3))^(x) ? A=

What is the value of A A when we rewrite (23)x+4−(23)x \left(\frac{2}{3}\right)^{x+4}-\left(\frac{2}{3}\right)^{x} as A⋅(23)x A \cdot\left(\frac{2}{3}\right)^{x} ?\newlineA= A=

View step-by-step helpView step-by-step help
Homeright chevron icon
Math Problemsright chevron icon
Algebra 1right chevron icon
Compare linear and exponential growthright chevron icon

Full solution

Q. What is the value of A A when we rewrite (23)x+4−(23)x \left(\frac{2}{3}\right)^{x+4}-\left(\frac{2}{3}\right)^{x} as A⋅(23)x A \cdot\left(\frac{2}{3}\right)^{x} ?\newlineA= A=
  1. Factor out common term: We need to factor out (23)x\left(\frac{2}{3}\right)^x from both terms in the expression (23)x+4−(23)x\left(\frac{2}{3}\right)^{x+4}-\left(\frac{2}{3}\right)^{x}.
  2. Rewrite using exponent property: First, we rewrite (23)x+4\left(\frac{2}{3}\right)^{x+4} as (23)x⋅(23)4\left(\frac{2}{3}\right)^x \cdot \left(\frac{2}{3}\right)^4 by using the property of exponents that states am+n=am⋅ana^{m+n} = a^m \cdot a^n.
  3. Factor out common term again: Now we have (23)x⋅(23)4−(23)x\left(\frac{2}{3}\right)^x \cdot \left(\frac{2}{3}\right)^4 - \left(\frac{2}{3}\right)^x. We can factor (23)x\left(\frac{2}{3}\right)^x out of both terms.
  4. Calculate value inside brackets: After factoring out (23)x\left(\frac{2}{3}\right)^x, we get (23)x⋅[(23)4−1].\left(\frac{2}{3}\right)^x \cdot \left[\left(\frac{2}{3}\right)^4 - 1\right].
  5. Substitute value into brackets: We calculate (23)4\left(\frac{2}{3}\right)^4 to find the value inside the brackets. (23)4=(24)/(34)=1681\left(\frac{2}{3}\right)^4 = \left(2^4\right)/\left(3^4\right) = \frac{16}{81}.
  6. Calculate final result: Substitute 1681\frac{16}{81} into the brackets: (23)x×(1681−1)\left(\frac{2}{3}\right)^x \times \left(\frac{16}{81} - 1\right).
  7. Calculate final result: Substitute 1681\frac{16}{81} into the brackets: (23)x×(1681−1)\left(\frac{2}{3}\right)^x \times \left(\frac{16}{81} - 1\right).Now we calculate 1681−1\frac{16}{81} - 1. Since 11 is equivalent to 8181\frac{81}{81}, we have 1681−8181=16−8181=−6581.\frac{16}{81} - \frac{81}{81} = \frac{16 - 81}{81} = -\frac{65}{81}.
  8. Calculate final result: Substitute 1681\frac{16}{81} into the brackets: (23)x×(1681−1)\left(\frac{2}{3}\right)^x \times \left(\frac{16}{81} - 1\right).Now we calculate 1681−1\frac{16}{81} - 1. Since 11 is equivalent to 8181\frac{81}{81}, we have 1681−8181=16−8181=−6581\frac{16}{81} - \frac{81}{81} = \frac{16 - 81}{81} = -\frac{65}{81}.The expression is now (23)x×(−6581)\left(\frac{2}{3}\right)^x \times \left(-\frac{65}{81}\right). Therefore, A=−6581A = -\frac{65}{81}.

More problems from Compare linear and exponential growth

Question
Jill bought a used motorcycle from a seller online for $1,200. The seller will charge her $5 a day to store the motorcycle at his house until she is able to pick it up. You can use a function to describe the total amount of money Jill will owe the seller if she waits xx days to pick up the motorcycle.\newlineWrite an equation for the function. If it is linear, write it in the form g(x)=mx+bg(x) = mx + b. If it is exponential, write it in the form g(x)=a(b)xg(x) = a(b)^x.\newlineg(x)=‾g(x) = \underline{\hspace{3em}}
Get tutor helpright-arrow

Posted 5 months ago

Question
How does f(t)=−2t−7f(t)=-2t-7 change over the interval from t=−7t=-7 to t=−6t=-6?\newlineChoices:\newline[f(t) decreases by 2]\left[\text{f(t) decreases by } 2\right]\newline[f(t) increases by 2]\left[\text{f(t) increases by } 2\right]\newline[f(t) increases by 200%]\left[\text{f(t) increases by } 200\%\right]\newline[f(t) decreases by a factor of 2]\left[\text{f(t) decreases by a factor of } 2\right]
Get tutor helpright-arrow

Posted 5 months ago

Question
How does g(t)=9tg(t)=9^t change over the interval from t=1t=1 to t=3t=3?\newlineChoices: \newline[g(t) decreases by a factor of 81]\left[\text{g(t) decreases by a factor of } 81\right]\newline[g(t) increases by a factor of 81]\left[\text{g(t) increases by a factor of } 81\right]\newline[g(t) increases by 18%]\left[\text{g(t) increases by } 18\%\right]\newline[g(t) decreases by 9%]\left[\text{g(t) decreases by } 9\%\right]
Get tutor helpright-arrow

Posted 5 months ago

Question
Both of these functions grow as xx gets larger and larger. Which function eventually exceeds the other?\newline Choices:\newline(A)f(x)=8x+3.3(A)f(x) = 8x + 3.3\newline(B)g(x)=3.3x−5(B)g(x) = 3.3^x - 5
Get tutor helpright-arrow

Posted 6 months ago

Question
Both of these functions grow as x x gets larger and larger. Which function eventually exceeds the other?\newlineChoices:\newline(A) f(x)=2x+9(A) \ f(x) = 2x + 9 \newline(B) g(x)=2x(B)\ g(x) = 2^x
Get tutor helpright-arrow

Posted 6 months ago

Question
The functions f(x) f(x) and g(x) g(x) are differentiable. \newlineThe function h(x) h(x) is defined as: h(x)=g(x)f(x) h(x)=\frac{g(x)}{f(x)} \newlineIf f(8)=1 f(8)=1 , f′(8)=−6 f'(8)=-6 , g(8)=8 g(8)=8 , and g′(8)=−10 g'(8)=-10 , what is h′(8) h'(8) ? \newlineSimplify any fractions. \newlineh′(8)= h'(8)= ______
Get tutor helpright-arrow

Posted 6 months ago

Question
The functions p(x) p(x) and q(x) q(x) are differentiable. \newlineThe function r(x) r(x) is defined as: r(x)=p(x)q(x) r(x)= \frac{p(x)}{q(x)} \newlineIf p(3)=2 p(3)= 2 , p′(3)=4 p'(3)= 4 , q(3)=6 q(3)= 6 , and q′(3)=9 q'(3)= 9 , what is r′(3) r'(3) ? \newlineSimplify any fractions. \newliner′(3)= r'(3)= _____
Get tutor helpright-arrow

Posted 7 months ago

Question
The functions u(x) u(x) and v(x) v(x) are differentiable. \newlineThe function w(x) w(x) is defined as: w(x)=u(x)v(x) w(x)= \frac{u(x)}{v(x)} \newlineIf u(5)=3 u(5)= 3 , u′(5)=−2 u'(5)= -2 , v(5)=7 v(5)= 7 , and v′(5)=1 v'(5)= 1 , what is w′(5) w'(5) ? \newlineSimplify any fractions. \newlinew′(5)= w'(5)= _____
Get tutor helpright-arrow

Posted 7 months ago

Question
The functions a(x) a(x) and b(x) b(x) are differentiable. \newlineThe function c(x) c(x) is defined as: c(x)=a(x)b(x) c(x)= \frac{a(x)}{b(x)} \newlineIf a(2)=4 a(2)= 4 , a′(2)=5 a'(2)= 5 , b(2)=1 b(2)= 1 , and b′(2)=−3 b'(2)= -3 , what is c′(2) c'(2) ? \newlineSimplify any fractions. \newlinec′(2)= c'(2)= _____
Get tutor helpright-arrow

Posted 7 months ago

Question
The functions m(x) m(x) and n(x) n(x) are differentiable. \newlineThe function o(x) o(x) is defined as: o(x)=m(x)n(x) o(x)= \frac{m(x)}{n(x)} \newlineIf m(7)=2 m(7)= 2 , m′(7)=−1 m'(7)= -1 , n(7)=4 n(7)= 4 , and n′(7)=8 n'(7)= 8 , what is o′(7) o'(7) ? \newlineSimplify any fractions. \newlineo′(7)= o'(7)= _____
Get tutor helpright-arrow

Posted 7 months ago

View all (427)

Related topics

Algebra - Order of OperationsAlgebra - Distributive Property`X` and `Y` AxesGeometry - Scalene TriangleCommon MultipleGeometry - Quadrant