Week 15 Quiz

Solve 2ˣ = 16 by matching bases.

Select one.

• x = 8
• x = 4
• x = 2
• x = 14

Which value of x checks when you substitute it into 3^(x + 1) = 27?

Select one.

• x = 2
• x = 3
• x = 8
• x = 26

Solve 9ˣ = 3^(x + 4).

Select one.

• x = 2
• no solution
• x = 4
• x = 8

Which is the exact solution of 2ˣ = 10?

Select one.

• 10 ⁄ 2
• ln 2 ⁄ ln 10
• 1 ⁄ ln 2
• ln 10 ⁄ ln 2

Solve log₂(x − 1) = 3.

Select one.

• x = 4
• x = 9
• x = 7
• x = 10

Solve log(x) + log(x − 3) = 1.

Select one.

• x = 5 only
• x = 5 or x = −2
• x = −2 only
• no solution

1,000 dollars grows at 6% compounded continuously, A = 1000 · e^(0.06t). About how long does it take to double?

Select one.

• exactly 12 years
• about 33.33 years
• about 11.55 years
• about 16.67 years

A sample decays as A = A₀ · e^(−0.15t), with t in hours. What is its half-life?

Select one.

• about −4.62 hours
• about 6.67 hours
• about 0.10 hours
• about 4.62 hours

Which substitution check confirms that x = 9 solves log₂(x − 1) = 3?

Select one.

• log₂(9 − 1) = log₂(8) = 3, because 2³ = 8
• log₂(9) = 3, because 9 ⁄ 3 = 3
• 9 − 1 = 3, because 8 is close to 3
• log₂(8) = 4, because 8 ⁄ 2 = 4

Select every true statement about continuous growth and decay times.

Select every option that applies.

• 5,000 dollars at 6% compounded continuously doubles in about 11.55 years
• A larger deposit takes longer to double at the same rate
• At 8% compounded continuously, the doubling time is about 8.66 years
• The rule of 72 gives the exact doubling time
• Tripling at 5% compounded continuously takes about 21.97 years