Lesson 4: Practice Problems

Mathematics

1 answer:

gtnhenbr [62]2 years ago

3 0

Answer:

a).1

b).1

c).111

Step-by-step explanation:

a) anything to the zero power is 1

b) any number divided by itself is one

c) 100+10+1=111

You might be interested in

A bacteria culture initially contains 100 cells and grows at a rate proportional to its size. After an hour the population has i

bija089 [108]

Answer: $\bold{a)\ P(t)=P_o\cdot e^{t\cdot ln(2.7)}}$

b) 5314

c) ln 2.7

d) 4.6 hrs

<u>Step-by-step explanation:</u>

$P(t) = P_o\cdot e^{kt}\\\\\bullet \text{P(t) is the number of bacteria after t hours} \\\bullet P_o\text{ is the initial number of bacteria}\\\bullet \text{k is the rate of growth}\\\bullet \text{t is the time (in hours)}\\\\\\270=100\cdot e^{k(1)}\\2.7=e^k\\ln\ 2.7=\ln e^k\\\boxed{ln\ 2.7=k}\\\\\text{So the equation to find the number of bacteria is: }\boxed{P(t)=P_o\cdot e^{t\cdot ln(2.7)}}\\\\\\P(4)=100\cdot e^{4\cdot ln(2.7)}\\.\qquad =\boxed{5314}$

$10,000=100\cdot e^{t\cdot ln(2.7)}\\100=e^{t\cdot ln(2.7)}\\ln\ 100=ln\ e^{t\cdot ln(2.7)}\\ln\ 100=t\cdot ln(2.7)\\\dfrac{ln\ 100}{ln\ 2.7}=t\\\\\boxed{4.6=t}$

4 0

3 years ago

Find the area of a triangle with a base length of 3 units and a height of 4 units.

svetlana [45]

Answer:

$6$ square units

Step-by-step explanation:

The area of a triangle can be calculated by multiplying the triangle's base by its height, and then dividing the result by $2$ . As an algebraic expression, this would be $\frac{bh}{2}$ , where $b$ is the triangle's base and $h$ is the triangle's height. In this case, we know that $b=3$ and $h=4$ . Therefore, the area of this triangle is $\frac{3*4}{2} =\frac{12}{2} =6$ square units. Hope this helps!