In 2009, there were 1570 bears in a wildlife refuge. in 2010, the population had increased to approximately 1884 bears. if this trend continues and the bear population is increasing exponentially, how many bears will there be in 2018?

Step-by-step explanation:

we know that

In this problem we have a exponential function of the form

where

x ----> is the number of years since 2009

y ----> is the population of bears

a ----> is the initial value

b ---> is the base

step 1

Find the value of a

For x=0 (year 2009)

y=1,570 bears

substitute

so

step 2

Find the value of b

For x=1 (year 2010)

y=1,884 bears

substitute

The exponential function is equal to

step 3

How many bears will there be in 2018?

2018-2009=9 years

so

For x=9 years

substitute in the equation

(sin 42)/31. = sinx)/37

sinx = 37 (sin42)/31

= 37× 0.66/31 = 0.787

x= 51.9

other angle opposite to y = 180-51.9-42

= 180- 93.9 =86.1

so

sin42)/31 = sin 86.1)/y

0.021 = 0.997 /y

y= 0.997/0.021 =47.47

d.) yes, because the volume of the cone is greater than the volume of the sphere

step-by-step explanation: