The number of bacteria in a petri dish is 524 and growing at a rate of 7% every month.

Mathematics

2 answers:

kicyunya [14]3 years ago

7 0

This is an exponential growth problem.
y = 524(1.07)^7
y = 841 bacteria after 7 months

lora16 [44]3 years ago

5 0

Month 0 = 524
Month 1 = 524 + (524*.07) = 560.68
Month 2 = 560.68 +(560.68*.07) = 599.9276
Month 3 = 599.9276 +(599.9276*.07) = 641.922532
Month 4 = 641.922532 +( 641.922532*.07) = 686.8571092
Month 5 = 686.8571092 +(686.8571092*.07) = 734.9371068
Month 6 = 734.9371068 +(734.9371068*.07) = 786.3827043
Month 7 = 786.3827043 +(786.3827043*.07) = 841.4294936

Round to nearest whole number = 841 bacteria in the petri dish.

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A garden box has a perimeter of 18½ feet. If the length is 5 feet, what is the area of the garden box?

Travka [436]

Answer:

$area=\frac{85}{4}feet^{2}$

Step-by-step explanation:

1. Approach

Since it is given that the garden box is a rectangle, then the opposite sides are congruent. One can use this to their advantage, by setting up an equation that enables them to solve for the width of the rectangle. After doing so, one will multiply the width by the given length and solve for the area.

2. Solve for the width

It is given that the garden box is a rectangle. As per its definition, opposite sides in a rectangle are congruent. The problem gives the length and the perimeter of the rectangle, therefore, one can set up an equation and solve for the width.

$perimeter=18\frac{1}{2}\\\\length=5$

$2(length+width)=perimeter$

Substitute,

$2(5+width)=18\frac{1}{2}$

Conver the mixed number to an improper fraction. This can be done by multiplying the "number" part of the mixed number by the denominator of the fraction. Then add the result to the numerator.

$2(5+width)=\frac{37}{2}$

Inverse operations,

$2(5+width)=\frac{37}{2}\\/2\\\\5+width=\frac{37}{4}\\-5\\\\width=\frac{17}{4}$

3. Solve for the area

Now that one has solved for the width of the box, one must solve for the area. This can be done by multiplying the length by the width. Since the width is a fraction, one must remember, that when multiplying an integer by a fraction, one will multiply the integer by the numerator (the top of the fraction), and then simplify by reducing the fraction, if possible. Reducing the fraction is when one divides both the numerator and the denominator by the GCF (Greatest Common Factor).

$length=5\\\\width = \frac{17}{4}$