Question

Give the starting value a, the growth factor b, and the growth rate r if Q = ab^t = a(1 + r)^t. Write r as a percent.

Q = 34.3 (0.788) Superscript t
[Options: a. a = 29.94, b = 0.788, r = 78.8%, b. a = 34.3, b = 0.788, r = 21.2%, c. a = 29.94, b = 0.212, r = 78.8%, d. a = 34.3, b = 0.212, r = 11.2%]

Answer 1

The starting value (a) is 34.3, the growth factor (b) is 0.788, and the growth rate (r), expressed as a percentage, is -21.2%. This represents a decay rate rather than a growth rate. Option b is the correct answer.

Step-by-step explanation:

The question requires us to identify the starting value a, growth factor b, and the growth rate r from the given exponential function Q = 34.3 (0.788)^t. Comparing it to the general form Q = ab^t = a(1 + r)^t it's clear that:

• The starting value a is 34.3,
• The growth factor b is 0.788.

To find the growth rate as a percent, we need to express b as 1 + r. So, 0.788 = 1 + r, which means r = -0.212 (since it's negative, this is actually a decay rate).

Converting the decimal to a percentage, r as a percent is -21.2%.

Therefore, the correct answer is:

• a = 34.3,
• b = 0.788,
• r = -21.2%.