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3 years ago

14

Pls help me ! Thanks!

1 answer:

Alik [6]3 years ago

4 0

Terms are the numbers and variables that are usually separated by an addition sign or a subtraction sign. In the expression 2x, 3y, 5z, and 4 are all terms.

Variables are the letters that come after a number. They represent the unknown number in the equation. The x, y, and z in the expression are the variables.

Coefficients are the numbers in front of the variables. For example, 2, 3, 5, and 4 are the coefficients.

The constants are the "signs" in between the terms. These include the addition sign and the subtraction sign.

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2 years ago

Solve the equation for x. 3/4(x + 21) = 10 1/2

CaHeK987 [17]

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Step-by-step explanation:

3/4(x+21)=10 1/2

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3 years ago

A bacteria culture grows with a constant relative growth rate. After 2 hours there are 400 bacteria and after 8 hours the count

Debora [2.8K]

Answer:

a) P(0) = 80

b) $P(t) = 80(2.2361)^t$

c) 22,363 cells.

d) The rate of growth after 7 hours is of 18,000 bacteria per hour.

e) 9.7 hours.

Step-by-step explanation:

A bacteria culture grows with a constant relative growth rate.

This means that the population is given by:

$P(t) = P(0)(1+r)^t$

In which P(0) is the initial population and r is the growth rate, as a decimal.

After 2 hours there are 400 bacteria and after 8 hours the count is 50,000.

This means that in 6 hours, the population went from 400 bacteria to 50,000 bacteria. We use this to find r. So

$50000 = 400(1+r)^6$

$(1+r)^6 = \frac{50000}{400}$

$(1+r)^6 = 125$

$\sqrt[6]{(1+r)^6} = \sqrt[6]{125}$

$1 + r = 125^{\frac{1}{6}}$

$1 + r = 2.2361$

So

$P(t) = P(0)(2.2361)^t$

(a) Find the initial population. P(0)

We have that P(2) = 400. We use this to find P(0). So

$P(t) = P(0)(2.2361)^t$

$400 = P(0)(2.2361)^2$

$P(0) = \frac{400}{(2.2361)^2}$

$P(0) = 80$

So

$P(t) = 80(2.2361)^t$

(b) Find an expression for the population after t hours.

$P(t) = 80(2.2361)^t$

(c) Find the number of cells after 7 hours.

This is P(7). So

$P(7) = 80(2.2361)^7 = 22363$

22,363 cells.

(d) Find the rate of growth after 7 hours.

We have to find the derivative when t = 7. So

$P(t) = 80(2.2361)^t$

$P^{\prime}(t) = 80\ln{2.2361}(2.2361)^t$

$P^{\prime}(7) = 80\ln{2.2361}(2.2361)^7 = 18000$

The rate of growth after 7 hours is of 18,000 bacteria per hour.

(e) When will the population reach 200,000?

This is t for which $P(t) = 200000$ . So

$P(t) = 80(2.2361)^t$

$200000 = 80(2.2361)^t$

$(2.2361)^t = \frac{200000}{80}$

$(2.2361)^t = 2500$

$\log{(2.2361)^t} = \log{2500}$

$t\log{2.2361} = \log{2500}$

$t = \frac{\log{2500}}{\log{2.2361}}$

$t = 9.7$

So 9.7 hours.

8 0

3 years ago