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:

If y=30(910)xy=30\left(\frac{9}{10}\right)^x is graphed in the xyxy-plane, which of the following characteristics of the graph is displayed as a constant or coefficient in the equation?\newlineChoose 11 answer:\newline(A) Slope\newline(B) The value yy approaches as xx decreases\newline(C) xx-intercept\newline(D) yy-intercept

View step-by-step helpView step-by-step help
Homeright chevron icon
Math Problemsright chevron icon
Calculusright chevron icon
Find equations of tangent lines using limitsright chevron icon

Full solution

Q. If y=30(910)xy=30\left(\frac{9}{10}\right)^x is graphed in the xyxy-plane, which of the following characteristics of the graph is displayed as a constant or coefficient in the equation?\newlineChoose 11 answer:\newline(A) Slope\newline(B) The value yy approaches as xx decreases\newline(C) xx-intercept\newline(D) yy-intercept
  1. Identify Graph Characteristic: We need to identify the characteristic of the graph of the equation y=30(910)xy=30\left(\frac{9}{10}\right)^x that is represented by a constant or coefficient in the equation. Let's analyze the given equation and the options provided.
  2. Exponential Function Analysis: The equation y=30(910)xy=30\left(\frac{9}{10}\right)^{x} is an exponential function. In an exponential function, the base of the exponent (in this case 910\frac{9}{10}) determines the rate of growth or decay, but it is not the slope of the graph. Therefore, option (A) Slope is not correct.
  3. Coefficient Interpretation: The coefficient 3030 in the equation y=30(910)xy=30\left(\frac{9}{10}\right)^{x} is the initial value of yy when x=0x=0. This means that when we graph the equation, the point where the graph intersects the yy-axis (the yy-intercept) is at y=30y=30. Therefore, option (D) yy-intercept is correct.
  4. Approaching Value Analysis: The value that yy approaches as xx decreases in the equation y=30(910)xy=30\left(\frac{9}{10}\right)^{x} is related to the horizontal asymptote of the graph. However, this value is not explicitly shown as a constant or coefficient in the equation. Therefore, option (B) The value yy approaches as xx decreases is not correct.
  5. X-Intercept Analysis: The xx-intercept of a graph is the value of xx where the graph crosses the xx-axis, which means y=0y=0. For the given equation y=30(910)xy=30\left(\frac{9}{10}\right)^x, solving for y=0y=0 would not result in a real number solution for xx, because the exponential function never actually reaches zero. Therefore, option (C)(C) xx-intercept is not correct.

More problems from Find equations of tangent lines using limits

Question
Consider the curve given by the equation xy2+5xy=50 x y^{2}+5 x y=50 . It can be shown that dydx=−y(y+5)x(2y+5).  \frac{d y}{d x}=\frac{-y(y+5)}{x(2 y+5)} \text {. } \newlineWrite the equation of the vertical line that is tangent to the curve.
Get tutor helpright-arrow

Posted 7 months ago

Question
What is the value of ddx(x−3) \frac{d}{d x}\left(x^{-3}\right) at x=3 x=3 ?
Get tutor helpright-arrow

Posted 3 months ago

Question
The rate of change dPdt \frac{d P}{d t} of the number of algae in a tank is modeled by the following differential equation:\newlinedPdt=231710614P(1−P662) \frac{d P}{d t}=\frac{2317}{10614} P\left(1-\frac{P}{662}\right) \newlineAt t=0 t=0 , the number of algae in the tank is 174174 and is increasing at a rate of 2828 algae per minute. At what value of P P is P(t) P(t) growing the fastest?\newlineAnswer:
Get tutor helpright-arrow

Posted 9 months ago

Question
The rate of change dPdt \frac{d P}{d t} of the number of bacteria in a tank is modeled by the following differential equation:\newlinedPdt=29849P(598−P) \frac{d P}{d t}=\frac{2}{9849} P(598-P) \newlineAt t=0 t=0 , the number of bacteria in the tank is 196196 and is increasing at a rate of 1616 bacteria per minute. At what value of P P does the graph of P(t) P(t) have an inflection point?\newlineAnswer:
Get tutor helpright-arrow

Posted 9 months ago

Question
The rate of change dPdt \frac{d P}{d t} of the number of people infected by a disease is modeled by the following differential equation:\newlinedPdt=45125404P(800−P) \frac{d P}{d t}=\frac{45}{125404} P(800-P) \newlineAt t=0 t=0 , the number of people infected by the disease is 214214 and is increasing at a rate of 4545 people per hour. What is the limiting value for the total number of people infected by the disease as time increases?\newlineAnswer:
Get tutor helpright-arrow

Posted 9 months ago

Question
The exponential function f f is graphed in the xy x y -plane. As x x increases by 1,y 1, y increases by a factor of 33 . Which of the following could be f f ?\newlineChoose 11 answer:\newline(A) f(x)=(13)x f(x)=\left(\frac{1}{3}\right)^{x} \newline(B) f(x)=(13)x+3 f(x)=\left(\frac{1}{3}\right)^{x}+3 \newline(C) f(x)=3x+2 f(x)=3^{x}+2 \newline(D) f(x)=2(3)x f(x)=2(3)^{x}
Get tutor helpright-arrow

Posted 2 months ago

Question
Which of the following is a correct interpretation of the expression \newline−4+13-4+13?\newlineChoose 11 answer:\newline(A) The number that is 44 to the left of −13-13 on the number line\newline(B) The number that is 44 to the right of −13-13 on the number line\newline(C) The number that is 1313 to the left of −4-4 on the number line\newline(D) The number that is 1313 to the right of −4-4 on the number line
Get tutor helpright-arrow

Posted 8 months ago

Question
The function f f is defined by f(x)=x3+2sin⁡(3x−3) f(x)=x^{3}+2 \sin (3 x-3) . Use a calculator to write the equation of the line tangent to the graph of f f when x=0.5 x=0.5 . You should round all decimals to 33 places.\newlineAnswer:
Get tutor helpright-arrow

Posted 9 months ago

Question
The function f f is defined by f(x)=x2−2x+3cos⁡(x2−x) f(x)=x^{2}-2 x+3 \cos \left(x^{2}-x\right) . Use a calculator to write the equation of the line tangent to the graph of f f when x=−2.5 x=-2.5 . You should round all decimals to 33 places.\newlineAnswer:
Get tutor helpright-arrow

Posted 9 months ago

Question
The function f f is defined by f(x)=x2+x−2sin⁡(2x) f(x)=x^{2}+x-2 \sin (2 x) . Use a calculator to write the equation of the line tangent to the graph of f f when x=3 x=3 . You should round all decimals to 33 places.\newlineAnswer:
Get tutor helpright-arrow

Posted 9 months ago

View all (44)

Related topics

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