A gardener purchases a ceramic planter, in the shape of a hemisphere, for a small batch of leftover annuals. The volume of a hemisphere is modeled by the function V = 2/3πr 3
<span>A. Write a model for the radius as a function of the volume. </span>
<span>B. The label on the planter says that it holds approximately 134 cubic inches of potting soil. What is the radius of the planter, rounded to the nearest inch? Use 3.14 for π </span>
<span>r = ∛[(3/2)V) / π] </span>
<span>134 = (2/3) (3/14) r^3 </span>
<span>r = ∛[(3/2) (134) / 3.14] ≈ 4.00 inches </span>
Answer:
$57,369
Step-by-step explanation:
We have been given that an amount of $53,000 is placed in an investment account that grows at a fixed rate of 2% (compound growth) per year. We are asked to find the amount in the account after 4 years.
To solve our given problem we will use compound interest formula.\
, where,
A = Final amount after t years,
P = Principal amount,
r = Annual interest rate in decimal form,
n = Number of times interest is compounded per year,
t = Time in years.
Let us convert our given rate in decimal form.
![2\%=\frac{2}{100}=0.02](https://tex.z-dn.net/?f=2%5C%25%3D%5Cfrac%7B2%7D%7B100%7D%3D0.02)
Upon substituting our given values in compound interest formula we will get,
![A=\$53,000(1+\frac{0.02}{1})^{1*4}](https://tex.z-dn.net/?f=A%3D%5C%2453%2C000%281%2B%5Cfrac%7B0.02%7D%7B1%7D%29%5E%7B1%2A4%7D)
![A=\$53,000(1+0.02)^{4}](https://tex.z-dn.net/?f=A%3D%5C%2453%2C000%281%2B0.02%29%5E%7B4%7D)
![A=\$53,000(1.02)^{4}](https://tex.z-dn.net/?f=A%3D%5C%2453%2C000%281.02%29%5E%7B4%7D)
![A=\$53,000*1.08243216](https://tex.z-dn.net/?f=A%3D%5C%2453%2C000%2A1.08243216)
![A=\$57368.90448\approx \$57,369](https://tex.z-dn.net/?f=A%3D%5C%2457368.90448%5Capprox%20%5C%2457%2C369)
Therefore, an amount of $57,369 will be in the account after 4 years.
Answer:
61 and -87
Step-by-step explanation:
If the numbers are x and x - 148, we can write the following equation:
x + x - 148 = -26
2x - 148 = -26
2x = 122
x = 61 so x - 148 = 61 - 148 = -87
The population size after 6 years and after 8 years are 147 and 169 population respectively
<h3>Exponential functions</h3>
The standard exponential function is expressed as y = ab^x
where
a is the base
x is the exponent
Given the function that represents the population size P (t) of the species as shown;
![p(t)=\frac{550}{1+5e^{-0.1t}} \\](https://tex.z-dn.net/?f=p%28t%29%3D%5Cfrac%7B550%7D%7B1%2B5e%5E%7B-0.1t%7D%7D%20%5C%5C)
For the population size after 6 years
![p(t)=\frac{550}{1+5e^{-0.1(6)}} \\P(6)=\frac{550}{3.744}\\ P(6)=147 population](https://tex.z-dn.net/?f=p%28t%29%3D%5Cfrac%7B550%7D%7B1%2B5e%5E%7B-0.1%286%29%7D%7D%20%5C%5CP%286%29%3D%5Cfrac%7B550%7D%7B3.744%7D%5C%5C%20P%286%29%3D147%20population)
For the population after 8 years
![p(t)=\frac{550}{1+5e^{-0.1(8)}} \\P(8)=\frac{550}{3.2466}\\ P(8)=169 population](https://tex.z-dn.net/?f=p%28t%29%3D%5Cfrac%7B550%7D%7B1%2B5e%5E%7B-0.1%288%29%7D%7D%20%5C%5CP%288%29%3D%5Cfrac%7B550%7D%7B3.2466%7D%5C%5C%20P%288%29%3D169%20population)
Hence the population size after 6 years and after 8 years are 147 and 169 population respectively
Learn more on exponential function here: brainly.com/question/2456547
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Answer:
where's the question???
Step-by-step explanation: