All categories

2 years ago

Write the exponential function y = 22(1.35)' in the form y = aekt.

Mathematics

1 answer:

vesna_86 [32]2 years ago

4 0

Answer:

y = 22·e^(0.3001t), growing
annual rate: 35%
continuous rate: 30.01%

Step-by-step explanation:

When an exponential function is in the form ...

y = ab^t

the factor 'b' is called the growth factor. When t is in years, it is related to the annual growth rate (r) by ...

b = 1 +r

In the alternate form, this can be written ...

y = a·e^(kt)

Comparing the forms, we see that ...

b = e^k ⇒ k = ln(b)

y = 22·1.35^t

k = ln(1.35) ≈ 0.3001

y = 22·e^(0.3001t)

The growth factor is greater than 1, so the function is growing.

The annual growth rate is ...

r = 1.35 -1 = 0.35 = 35.00%

The continuous growth rate is ...

k = 0.3001 = 30.01%

You might be interested in

Emma is planning a surprise party. she is considering.......

Ann [662]

Answer:

Step-by-step explanation:

what is she considering? I would need more information to complete the probolem

5 0

2 years ago

Read 2 more answers

A number cube has faces numbered 1 through 6, and a coin has two sides, "heads" and "tails". The

Mama L [17]

Answer:

The <em>required probability</em> is $\dfrac{1}{12}$ .

Step-by-step explanation:

Let <em>A </em>be the event of rolling the number cube.

Let <em>B</em> be the event of tossing the coin.

Total number of possibilities of rolling the number cube and tossing the coin are <em>12 </em>here.

$\{(1,H),(2,H),(3,H),(4,H),(5,H),(6,H),(1,T),(2,T),(3,T),(4,T),(5,T),(6,T)\}$

where <em>H</em> means Head on toss of coin and <em>T</em> means Tails on toss of coin.

Formula for probability of an event <em>E</em> is:

$P(E) = \dfrac{\text{Number of favorable cases}}{\text {Total number of cases}}$

Here, we have to find the probability of event 'E' i.e. getting a 6 on number cube and heads on coin.

Number of favorable cases are <em>1 </em>and total cases are <em>12</em>.

$\Rightarrow P(E) = \dfrac{1}{12}$

6 0

2 years ago

Mealworms are a healthy food for wild song birds. Adam buys a 3 oz container of mealworms for $7.35. Marco buys a 5 oz container

Artemon [7]

Answer: 5 oz

Step-by-step explanation:

you get more and for the price of 7.35 it’s not worth only getting three oz

3 0

2 years ago

Need help question 4

zysi [14]

You need to find what 3 is if 5 is $520,000
$520,000 divided by 5 = 104,000
104,000 x 3 = 312,000

Therefore 3 is 312,000
Hope this helps :3

5 0

3 years ago

What are tree diagrams? How can we use them in real life?

Phoenix [80]

Answer:

You can use tree diagrams to find the probability of something

3 0

2 years ago

Read 2 more answers