Question

Advertisers want to create "awareness," which is whether a consumer even knows about a business. If your business starts with 3% awareness and grows awareness by 5% per week (compounded), how long will it take to reach 75% awareness? The formula for compound growth is E = B x (1 + R)T, where E is ending value, B is beginning value, R is rate of growth, and T is the amount of time.

Can someone give a detailed explanation step by step as well? Thank you!

Answer 1

To find out how long it will take to reach 75% awareness, we can use the compound growth formula E = B x (1 + R)^T. By plugging in the given values, we can solve for the amount of time required. After performing the calculations, we find that it will take approximately 28.4 weeks to reach 75% awareness.

Step-by-step explanation:

To calculate how long it will take to reach 75% awareness, we can use the compound growth formula: E = B x (1 + R)^T.

In this case, the beginning value (B) is 3%, the rate of growth (R) is 5%, and the ending value (E) is 75%. We need to solve for the amount of time (T).

Using the compound growth formula, we have: 75 = 3 x (1 + 0.05)^T.

Take the natural logarithm on both sides to isolate T, and then solve for T: T = ln(75/3) / ln(1.05).

Using a calculator, T is approximately 28.4 weeks.