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2 years ago

I need help on number 2

Mathematics

1 answer:

Nina [5.8K]2 years ago

7 0

9514 1404 393

Answer:

a. 405

b. -2

c. 5

d. 43

Step-by-step explanation:

I don't like doing arithmetic any more than you do, so I let a calculator do it for me. A spreadsheet works well for this, too. The function values are shown in the attachment.

Put the function argument where the variable is and do the arithmetic.

a. h(4) = 5·3^4 = 405

b. d(2) = 7 -9(2 -1) = -2

c. h(0) = 5·3^0 = 5

d. d(-3) = 7 -9(-3 -1) = 43

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A lake currently has a depth of 30 meters. As sediment builds up in the lake, its depth decreases by 2% per year. This situation

lubasha [3.4K]

Answer:

This situations represents the depth of the lake after t years.

The rate of decay is equal to 0.02 a year.

So the depth of the lake each year is 0.98 times the depth in the previous year.

It will take 5.77 years for the depth of the lake to reach 26.7 meters.

Step-by-step explanation:

Exponential equation of decay:

The exponential equation for the decay of an amount is given by:

$D(t) = D(0)(1-r)^t$

In which D(0) is the initial amount and r is the decay rate, as a decimal.

A lake currently has a depth of 30 meters. As sediment builds up in the lake, its depth decreases by 2% per year.

This means that $D(0) = 30, r = 0.02$

$D(t) = D(0)(1-r)^t$

$D(t) = 30(1-0.02)^t$

$D(t) = 30(0.98)^t$

This situation represents

The depth of the lake after t years.

The rate of growth or decay, r, is equal to

The rate of decay is equal to 0.02 a year.

So the depth of the lake each year is times the depth in the previous year.

1 - 0.02 = 0.9

So the depth of the lake each year is 0.98 times the depth in the previous year.

It will take between years for the depth of the lake to reach 26.7 meters.

This is t for which D(t) = 26.7. So

$D(t) = 30(0.98)^t$

$26.7 = 30(0.98)^t$

$(0.98)^t = \frac{26.7}{30}$

$\log{(0.98)^t} = \log{\frac{26.7}{30}}$

$t\log{(0.98)} = \log{\frac{26.7}{30}}$

$t = \frac{\log{\frac{26.7}{30}}}{\log{0.98}}$

$t = 5.77$

It will take 5.77 years for the depth of the lake to reach 26.7 meters.

4 0

2 years ago

the bill for dinner was $150 if Romy paid in entire Bill and left 20% tip how much did Romy make pay in all

navik [9.2K]

Hello!

First, you'll need to find 20% of 150. You can do this by converting 20% into a decimal. To do so, you'll need to move the decimal place twice to the left to get 0.20. Now you'll need to multiply 150 by 0.20. Once you've done that, you should get $30. Now to find how much Romy paid in total, you'll need to add $30 to $150.

Romy in total payed $180 for the bill

I hope this helps!

6 0

3 years ago

If you answer yo get 20 points

Elodia [21]

Answer:

n = 2 + 2√3 and n = 2 - 2√3

Step-by-step explanation:

Let the number be n.

Then n² + 1 = 4n.

Rearranging this in proper quadratic format:

n² - 4n + 1

Here the coefficients are a = 1, b = -4 and c = 1.