Nonlinear Functions MCQ Quiz in తెలుగు - Objective Question with Answer for Nonlinear Functions - ముఫ్త్ [PDF] డౌన్‌లోడ్ కరెన్

The area of a rectangle is given by the formula $A=l\times w$, where $l$ is the length and $w$ is the width. Here, the length $l=2w$. Therefore, the area can be written as $A=2w\times w=2w^2$. Given that the area is $288$ square units, we can set up the equation $2w^2=288$. Solving for $w$, we divide both sides by 2 to get $w^2=144$. Taking the square root of both sides gives $w=12$. Therefore, the correct answer is $w=16$, making option 3 correct.

The function $p(n)=300,000(1.12{)}^n$ provides the profit $n$ years after the product launch. $p(7)\approx 545,616$ implies that after 7 years, the profit is approximately $545,616$ dollars.

Option 1 is correct, as it directly reflects the profit at $n=7$. 

The function $R(t)=350\times (1.05{)}^{\frac{3}{5}t}$ describes revenue growth. To find the percentage increase every 10 months, calculate how many years 10 months is: $\frac{10}{12}=\frac{5}{6}$ of a year. Substitute $t=\frac{5}{6}$ into the function: $R(\frac{5}{6})=350\times (1.05{)}^{\frac{3}{5}\times \frac{5}{6}}=350\times (1.05{)}^{\frac{1}{2}}$. This results in approximately 1.03, indicating a 3% increase. Therefore, the revenue increases by 3% every 10 months.

Substitute $t=5$ into $h(t)=-4.9t^2+50t+5$. Compute $-4.9(5{)}^2+50(5)+5$. $5^2=25$, so $-4.9\times 25=-122.5$. Then, $50\times 5=250$. $-122.5+250+5=132.5$. Therefore, $h(5)=132.5$. The correct answer is 132.5.

Evaluate $s(x)$ for each $x$ value and subtract 6. For $x=-5$, $s(-5)=(-5+1)(-5-4)(-5+5)=-4\times -9\times 0=0$, so $y=0-6=-6$. For $x=-1$, $s(-1)=(-1+1)(-1-4)(-1+5)=0\times -5\times 4=0$, hence $y=0-6=-6$. For $x=4$, $s(4)=(4+1)(4-4)(4+5)=5\times 0\times 9=0$, thus $y=0-6=-6$. The correct table is therefore Option 4, which shows $y=-6$ for each $x$.

The function $g(x)=200(1.05{)}^x$ models exponential growth of an investment. $g(6)$ represents the value of the investment 6 years after the initial amount was invested. Calculating $g(6)$, we get $g(6)=200(1.05{)}^6$, which is approximately 268. This means that after 6 years, the value of the investment is approximately 268 dollars. Therefore, option 1 is correct. Option 2 is incorrect because it suggests the value increased by 268 dollars, not that it became 268 dollars. Option 3 is incorrect because it implies multiplication by the original value rather than the current value. Option 4 is incorrect because it refers to a percentage increase over a single year, not over 6 years.

The function $h(t)=9t^2$ describes the height of a ball as a function of time $t$. Thus, $h(3)=81$ implies that after $3$ seconds, the ball reaches a height of $81$ feet. Option 1 correctly interprets this situation, while the other options present incorrect relationships between time and height or misstate the initial or maximum conditions.

The function $h(t)=1200(0.95{)}^t$ models exponential decay, meaning the population decreases each year by a certain percentage. $h(3)$ represents the population 3 years after the project began. Calculating $h(3)=1200(0.95{)}^3$, we get $h(3)$ which is approximately 1083. Thus, option 1 is correct because it interprets $h(3)$ as the fish population being approximately 1083 after 3 years. Option 2 is incorrect because it implies a decrease of 1083 rather than a value of 1083. Option 3 is incorrect as it misinterprets the multiplication factor. Option 4 is incorrect as it misrepresents the yearly decrease as applying to only one year.

To find the equation of the parabola, we use the vertex form $y=a(x-h{)}^2+k$, where $(h,k)$ is the vertex. Given $(h,k)=(3,5)$, the equation becomes $y=a(x-3{)}^2+5$. The parabola passes through $(5,1)$, so substitute $x=5$ and $y=1$ into the equation: $1=a(5-3{)}^2+5$. This simplifies to $1=4a+5$, giving $-4=4a$, so $a=-1$. Therefore, the equation is $y=-1(x-3{)}^2+5$. Option 3 is incorrect because $a=-0.5$ does not satisfy the equation with the given point, while Option 4 represents an upward-opening parabola.

The function $p(x)=50000(1.02{)}^x$ describes exponential growth of a city's population. $p(5)$ estimates the population 5 years after 2015. Calculating $p(5)$, we find $p(5)=50000(1.02{)}^5$, approximately 55204. This means that in the year 2020, the population is about 55204, making option 1 correct. Option 2 is incorrect as it mistakenly suggests a multiplication by 55204. Option 3 is incorrect as it implies an addition rather than a final value. Option 4 is incorrect because it correctly states the growth rate but does not interpret the specific output of the function.