Question

Given the formula Q = ab', where Q is the final value, a is the starting value, b is the growth factor, and r is the growth rate, expressed as a percent. Identify the correct values for a, b, and r:

a. a = 29.94, b = 0.788, r = 78.8%
b. a = 34.3, b = 0.212, r = 21.2%
c. a = 29.94, b = 0.788, r = 21.2%
d. a = 34.3, b = 0.212, r = 78.8%

Answer 1

None of the options provided have the correct combination of values for a, b, and r according to the growth formula since the growth factor 'b' must be 1 plus the growth rate in its decimal form.

Step-by-step explanation:

The task is to find the correct values for a, b, and r in the formula Q = abr. Looking at the options provided, we notice that the growth rate, r, is expressed as a percent, whereas in the growth factor 'b' it has to be in decimal form which is equal to 1 + growth rate (in decimal form, not as a percent).

In case of a growth rate of 78.8%, the corresponding decimal form would be 0.788, making the growth factor b = 1 + 0.788 = 1.788, not b = 0.788 as it is listed in option a and c. Similarly, for a growth rate of 21.2%, we'd have b = 1 + 0.212 = 1.212, not b = 0.212 as stated in options b and d.

Therefore, none of the options provided have the correct combination of values for a, b, and r as per the described formula Q = abr.