IM 3 Test

The equation below shows that the value of a $4,800 certificate of deposit (CD) n years in the future will be $5,000:

5,000=4,800(1+0.03)ⁿ

How many years must pass before the CD will have a value of $5,000? (round to the tenth place)

BONUS: The dollar value of an annuity investment is modeled by the function below, where n is the number of years since the annuity was purchased.

A(n)=25,000(1+0.06)ⁿ

What is the domain of the inverse of this function?

• A ≥ 0

• A > 0

• A ≥ 25,000

• 0 < A < 25,000

The exponential growth of a particular strain of bacteria is modeled by the equation 1,000=100e⁵ᵏ, where 1,000 represents the number of bacteria present after 5 hours have passed.

Which of these represent the growth rate, k, of the bacteria? Select TWO that are correct.

• ln (10) / 5

• ln (200) / 100

• log 2

• 20% per hour

• 46% per hour

BONUS: The population of a city since the year 2000 is modeled by the function below, where x is the number of years since 2000:

P(x)=120,000e⁻⁰.⁰¹ˣ

Which correctly compares the function on the intervals 5 ≤x ≤10 and 15 ≤ x ≤ 20?

• The average rate of change of the function is greater on the interval 5 ≤ x ≤ 10 than on the interval 15 ≤ x ≤ 20.

  
  

• The average rate of change of the function is greater on the interval 15 ≤ x ≤ 20 than on the interval 5 ≤ x ≤ 10.

  
  

• The value of the function changes by a greater percentage on the interval 15 ≤ x ≤ 20 than on the interval 5 ≤ x ≤ 10.

• The value of the function changes by a greater percentage on the interval 5 ≤ x ≤ 10 than on the interval 15 ≤ x ≤ 20.

  
  

A random sample of 30 students had a final exam mean score of 86 with a standard deviation of 2 points. What percentage of the students scored between 84 and 88 if the scores are normally distributed? (round to the tenth place)

Which trigonometric ratio can be used to find the length of the side of the triangle labeled x?

• tan 67

• cos 23

• sin 67

• sin 23

Consider triangle ABC, shown below, where the length of side BC is 6 cm, ∠A is 52°, and ∠C is 36°.

Find the length of side AC. Round to the nearest tenth.

What is the length of the path, to the nearest foot?

A lizard that is one standard deviation above the mean is ______ long.

What relationship exists between b/c and q/r

• They may not be equal because the measures of ∠B and ∠Q may not be equal.

• They are equal because they are both right triangles.

• They are equal because the triangles are similar.

• They may not be equal because a and p may not be equal.