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TEA [102]
2 years ago
15

Imagine a population of birds with an initial size of 100, a per-capita birth rate of 2, and a per-capita death rate of 1 per ye

ar. Use the discrete time form of the exponential growth equation to predict the number of individuals in this population after 5 years of growth.
Mathematics
1 answer:
Soloha48 [4]2 years ago
8 0

Answer:

3200

Step-by-step explanation:

Given that:

The initial population of birds N_0 = 100

The time duration t = 5 years

Growth rate (r) = (Birth - Death) rate

= 2 - 1

= 1 / year

∴

using the discrete-time form:

N_t = N_o (1 + r )^t

N_t = 100 (1 + 1 )^5

N_t = 100 (2 )^5

N_t = 100 \times 32

N_t = 3200

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Suppose you work at a retail store that sells teddy bears. You always work 40 hours a week. The amount of your weekly paycheck i
brilliants [131]

a. Remember that f(x) is the amount of money you earned each week. Also note that teddybears = x

<em>f(x) = 5x + 300</em> is your equation

5x + 300 is your expression

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b. A reasonable domain can be 0 < x < 50, in which x is the amount you sell. 50 is a bit far out, but it takes into account holidays, as well as places you may sell at that have large amount of people.

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c. f(20) means that you sold 20 teddy bears, as 20 replaces x, which (like what was stated above) is the amount you sell

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d. Plug in 25 for x.

5x + 300 = t (total amount you make)

5(25) + 300 = t

Remember to follow PEMDAS. First, multiply 5 with 25

5 x 25 = 125

Next, add

125 + 300 = t

t = 425

$425 is the amount you make in a week.

-----------------------------------------------------------------------------------------------------------------

e. Note that you make $425 if you sell 25 teddy bears. Also remember that you are paid a flat $300. Remember the formula:

f(x) = 5x + 300

Plug in 425 for f(x)

425 = 5x + 300

Isolate the x. Do the opposite of PEMDAS. Note the equal sign. What you do to one side, you do to the other.

First, subtract 300 from both sides

425 (-300) = 5x + 300 (-300)

425 - 300 = 5x

125 = 5x

Next, divide 5 from both sides

(125)/5 = (5x)/5

x = 125/5

x = 25

25 teddy bears must be sold

-----------------------------------------------------------------------------------------------------------------

hope this helps

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