Max wrote an algorithm that searches for a specific term within a large set of terms. The following function gives the length of the search, in number of steps, over a set with n terms: S(n)=1.6*ln(0.9 n) What is the instantaneous rate of change of the search length for a set of 10 terms? Choose 1 answer: (A) 0.16 steps per term (B) 0.16 steps per second (C) 3.5 steps per term (D) 3.5 steps per second

Differentiate S(n): To find the instantaneous rate of change, we need to differentiate the function S(n) with respect to n. S(n) = 1.6 * ln(0.9n) Let's find S'(n), the derivative of S(n).Apply Chain Rule: Using the chain rule, the derivative of ln(0.9n) is 1/(0.9n) times the derivative of 0.9n, which is 0.9. So, S'(n) = 1.6 * (1/(0.9n)) * 0.9Simplify S'(n): Simplify the expression to find S'(n). S'(n) = 1.6 * (0.9/(0.9n))Evaluate at n=10: Cancel out the 0.9 in the numerator and denominator. S'(n) = 1.6 * (1/n)Calculate S'(10): Now we need to evaluate S'(n) at n = 10 to find the instantaneous rate of change when there are 10 terms. S'(10) = 1.6 * (1/10)Final Result: Calculate the value of S'(10). S'(10) = 1.6 * 0.1S'(10) = 0.16 This is the instantaneous rate of change of the search length when there are 10 terms.

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Max wrote an algorithm that searches for a specific term within a large set of terms. The following function gives the length of the search, in number of steps, over a set with $n$ terms: $\newline$ $S(n)=1.6 \cdot \ln (0.9 n)$ $\newline$ What is the instantaneous rate of change of the search length for a set of $10$ terms? $\newline$ Choose $1$ answer: $\newline$ (A) $0$ . $16$ steps per term $\newline$ (B) $0$ . $16$ steps per second $\newline$ (C) $3$ . $5$ steps per term $\newline$ (D) $3$ . $5$ steps per second

View step-by-step help

Home

Math Problems

Grade 7

Volume of cubes and rectangular prisms: word problems

Full solution

Q. Max wrote an algorithm that searches for a specific term within a large set of terms. The following function gives the length of the search, in number of steps, over a set with

n

terms:

\newline

S(n)=1.6 \cdot \ln (0.9 n)

\newline

What is the instantaneous rate of change of the search length for a set of

10

terms?

\newline

Choose

1

answer:

\newline

(A)

0

16

steps per term

\newline

(B)

0

16

steps per second

\newline

(C)

3

5

steps per term

\newline

(D)

3

5

steps per second

Differentiate $S(n)$ : To find the instantaneous rate of change, we need to differentiate the function $S(n)$ with respect to $n$ . $\newline$ $S(n) = 1.6 \cdot \ln(0.9n)$ $\newline$ Let's find $S'(n)$ , the derivative of $S(n)$ .
Apply Chain Rule: Using the chain rule, the derivative of $\ln(0.9n)$ is $\frac{1}{(0.9n)}$ times the derivative of $0.9n$ , which is $0.9$ . So, $S'(n) = 1.6 \times \left(\frac{1}{(0.9n)}\right) \times 0.9$
Simplify $S'(n)$ : Simplify the expression to find $S'(n)$ . $S'(n) = 1.6 \times (\frac{0.9}{0.9n})$
Evaluate at $n=10$ : Cancel out the $0.9$ in the numerator and denominator. $\newline$ $S'(n) = 1.6 \times (1/n)$
Calculate $S'(10)$ : Now we need to evaluate $S'(n)$ at $n = 10$ to find the instantaneous rate of change when there are $10$ terms. $\newline$ $S'(10) = 1.6 \times (\frac{1}{10})$
Final Result: Calculate the value of $S'(10)$ . $S'(10) = 1.6 \times 0.1$
Final Result: Calculate the value of $S'(10)$ . $\newline$ $S'(10) = 1.6 \times 0.1S'(10) = 0.16$ $\newline$ This is the instantaneous rate of change of the search length when there are $10$ terms.