Question

by converting to an exponential expression, solve \\(\log_3(x + 9) = 5\\).

a) \\(x = 234\\)
b) \\(x = 243\\)
c) \\(x = 114\\)
d) \\(x = \log_3(243)\\)

question 16 (5 points)
suppose that a population begins at a size of 100 and grows continuously at a rate of 200% per year. give the formula for calculating the size of that population after \\(t\\) years.

a) \\(a = 100 + 2e^t\\)
b) \\(a = 100 + e^{2t}\\)
c) \\(a = 100 + te^2\\)
d) \\(a = 100e^{2t}\\)

question 17 (5 points)
solve \\(e^x = e^{2x + 5}\\).

a) \\(x = -2\\)
b) \\(x = 10\\)
c) \\(x = 5\\)
d) \\(x = -5\\)

Explanation:

Convert logarithmic equation to exponential form

$$
LATEXBLOCK0
$$

Model continuous exponential growth

$$
LATEXBLOCK1
$$

Solve exponential equation with equal bases

$$
LATEXBLOCK2
$$

Answer:

Question 1

• A) \(x = 234\) (Correct answer)
• B) \(x = 243\)
• C) \(x = 114\)
• D) \(x = \log_3(243)\)

Question 16

• A) \(A = 100 + 2e^t\)
• B) \(A = 100 + e^{2t}\)
• C) \(A = 100 + te^2\)
• D) \(A = 100e^{2t}\) (Correct answer)

Question 17

• A) \(x = -2\)
• B) \(x = 10\)
• C) \(x = 5\)
• D) \(x = -5\) (Correct answer)