Question

Ellie is the agricultural manager of Apple a Day Orchards. To boost pollination, she puts a beehive with about 10,000 bees on the property. She expects the bee population to increase by 12% each year. You can use a function to approximate the number of bees in the hive after x years.
Write an equation for the function. If it is linear, write it in the form f(x)=mx+b. If it is exponential, write it in the form f(x)=a(b)x.

Answer 1

The population grows by a constant factor each year, so it's exponential. With initial population 10,000 and annual growth 12% (factor 1.12),

f(x) = 10000(1.12)^x.

(Here f(x) is the number of bees after x years; f(1)=11,200.)