The cost of a pound of strawberries at a local market increases at a rate of 2.1% per year due to greater agricultural costs. The following exponential expression gives the cost of a pound of strawberries after t years. 3.50(1.021)^t Which of the following expressions reveals the monthly rate of increase for the cost of a pound of strawberries?

1 - (1.021)^(1/12) ≈ 0.17 %

Step-by-step explanation:

In the given expression 3.50 is the initial value (cost per pound at the time of the first recording) and (1.021)^t is the increase factor for a given time difference since first recording (in years).

Putting into that expression yields the increase factor per month and subtracting it from 1 yields the “rate” notation which is just the part that was “added” to the initial amount.

Bonus: is the cost function for a given time in months.

Note that this approach gives you an increase rate based on an average month length. It doesn’t consider that a real month has different amount of days. For example “s = 3” means “3/12 of a year”, or “1/4 of a year” as opposed to something like “June 13 till September 13”.

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