Suppose a population of honey bees in ephraim, ut has an initial population of 2300 and 12 years later the population reaches 13000. use an explicit exponential model to find the rate of growth and common ratio for the honey bee population. express the rate of growth as a percentage. round to the nearest tenth. express the common ratio as a decimal. round to the nearest thousandth.

common ratio: 1.155

rate of growth: 15.5 %

Step-by-step explanation:

The model for exponential growth of population P looks like:

where is the population at time "t",

is the initial (starting) population

is the common ratio,

and is the rate of growth

Therefore, in our case we can replace specific values in this expression (including population after 12 years, and  initial population), and solve for the unknown common ratio and its related rate of growth:

This (1+r) is the common ratio, that we are asked to round to the nearest thousandth, so we use: 1.155

We are also asked to find the rate of increase (r), and to express it in percent form. Therefore we use the last equation shown above to solve for "r" and express tin percent form:

So, this number in percent form (and rounded to the nearest tenth as requested) is: 15.5 %

45.36 feet per second.

step-by-step explanation:

to find the most accurate determination for the number of feet per second tyrone traveled on his way to work let us convert miles to feet and minutes to seconds.

1 mile = 5280 feet.

1 minute = 60 seconds.

now we will divide 158400 by 3492 to find the most accurate determination for the number of feet per second tyrone traveled on his way to work.

therefore, tyrone traveled on his way to work at the rate of 45.36 feet per second.