Question

Writing an exponential function with a time cycle.

Write the exponential equation for each:

A. You have 12 units, and it triples every 4 days.
B. You have 2 units, and it grows by a factor of 1.5 every 3 weeks.
C. You have $5000 in your account, and lose 20% every 3 months.

Answer 1

To write the exponential equation for each scenario, we need to identify the base and the growth/decay factor.

Step-by-step explanation:

To write the exponential equation for each scenario, we need to identify the base and the growth/decay factor.

A. In scenario A, we start with 12 units and it triples every 4 days. This means the base is 3 (since it triples) and the time cycle is 4 days. The exponential equation is y = 12 * (3)^(t/4), where y is the final amount of units and t is the time in days.

B. In scenario B, we start with 2 units and it grows by a factor of 1.5 every 3 weeks. This means the base is 1.5 (since it grows by a factor of 1.5) and the time cycle is 3 weeks. The exponential equation is y = 2 * (1.5)^(t/3), where y is the final amount of units and t is the time in weeks.

C. In scenario C, we start with $5000 in an account and lose 20% every 3 months. This means the base is 0.8 (since we lose 20%) and the time cycle is 3 months. The exponential equation is y = 5000 * (0.8)^(t/3), where y is the final amount of money in the account and t is the time in months.