The population of frogs in a park is decreasing exponentially at a rate of 6% each year. in the year 2007, the population was estimated to be 5500. a. use the exponential decay formula to write an equation to model the situation. b. use your equation from part a to predict the frog population in the year 2018. c. sketch the graph of the equation you wrote in part a. find its asymptote, domain, and range.

a. Since, the exponential decay formula is,

Where, a is the initial value,

r is the decay rate per period,

x is the number of periods,

Suppose, the population is estimated from the year 2007,

Given,

The population in 2007 is, a = 5500,

Annual rate of decay, r = 6% = 0.06,

Hence, the population after x years,

Which is the required equation.

b. for 2018, x = 11 ( number of years since 2007 ),

Thus, the population in 2018 would be,

c. The graph of shown below,

Having no vertical asymptote,

And, horizontal asymptote is y=0

Domain = All possible value of x = { x | x ≥ 0 },

Range = All possible value of y = { y | 0 ≤ y ≤ 5500 }

75

step-by-step explanation:

you do x-29=46 (the number of cantaloupes sold)

in order to find x, you have to find what minus 29 equals 46, meaning you'd have to add 29 to 46.

29+46=75

if you replace x with 75, the equation looks like:

75-29=46

x=75

"it's not the heat, it's the humidity".   that's a partly valid phrase you may have heard in the summer, but it's actually both.   the heat index, also known as the apparent temperature, is what the temperature feels like to the human body when relative humidity is combined with the air temperature.   this has important considerations for the human body's comfort.   when the body gets too hot, it begins to perspire or sweat to cool itself off.   if the perspiration is not able to evaporate, the body cannot regulate its temperature.   evaporation is a cooling process.   when perspiration is evaporated off the body, it effectively reduces the body's temperature.   when the atmospheric moisture content (i.e. relative humidity) is high, the rate of perspiration from the body decreases.   in other words, the human body feels warmer in humid conditions.   the opposite is true when the relative humidity decreases because the rate of perspiration increases.   the body actually feels cooler in arid conditions.   there is direct relationship between the air temperature and relative humidity and the heat index, meaning as the air temperature and relative humidity increase (decrease), the heat index increases (decreases).

step-by-step explanation: