Mathematics, 02.02.2021 02:00 Woodsydal2390

A bacterial culture is known to grow at a rate proportional to the amount present. After one hour, there are 1000 strands of bacteria and after four hours, 3000 strands. Find an expression for the number of strands present in the culture at any time t. What is the initial number of strands

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Answer from: Shayleechase

The equation becomes y=694(1.44)^t . The initial number of strands is 694.

An exponential growth is in the form:

y = abˣ

where y, x are variables, a is the initial value of y and b is the multiplier.

Let y represent the number of strands after t hours.

After one hour, there are 1000 strands of bacteria:

1000 = ab¹

ab = 1000 (1)

After four hour, there are 3000 strands of bacteria:

3000 = ab⁴

ab⁴ = 3000 (2)

Dividing equation 2 by 1:

b³ = 3

b = 1.44

ab = 1000

a = 1000/b = 1000/1.44 = 694

The equation becomes y=694(1.44)^t

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Answer from: sheila54

The expression is: $P(t) = 693e^{0.3662t}$

The initial number of strands is 693

Step-by-step explanation:

A bacterial culture is known to grow at a rate proportional to the amount present.

This means that the bacterial model can be modeled by the following equation:

$P(t) = P(0)e^{rt}$

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

After one hour, there are 1000 strands of bacteria

This means that P(1) = 1000 , So

$P(0)e^{r} = 1000$

$P(0) = \frac{1000}{e^{r}}$

After four hours, 3000 strands.

This means that P(4) = 3000. So

$P(0)e^{4r} = 3000$

Since $P(0) = \frac{1000}{e^{r}}$ , we have that:

$\frac{1000}{e^{r}}e^{4r} = 3000$

$\frac{e^{4r}}{e^{r}} = \frac{3000}{1000}$

$e^{4r-r} = 3$

$e^{3r} = 3$

$\ln{e^{3r}} = \ln{3}$

$3r = \ln{3}$

$r = \frac{\ln{3}}{3}$

r = 0.3662

The initial population is:

$P(0) = \frac{1000}{e^{0.3662}} = 693$

The expression is:

$P(t) = 693e^{0.3662t}$

Answer from: Quest

a. turk and mcalister

b. howard, mission, and market

c. yes. since streets end some do not cross yet are not parallel to others. example: mcalister and 5th

step-by-step explanation:

parallel lines are lines which do not intersect ever and look a lot like railroad tracks. turk, mcalister and golden gate are examples of these.

intersect are streets which cross each other and a car on one can reach the other. howard, mission, and market intersect with 6th.

skew lines are lines which neither intersect nor are parallel. these lines exist here because some streets end and never intersect another like mcalister and 5th.

A. name the streets that are parallel to golden gate. b. name the streets that intersect 6th street.

Answer from: Quest

may i see the picture? it would a lot, xox

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