Mathematics, 03.02.2020 06:53 aprilhood4022

The price of gold has increased by 35% per year from 2000. in the year 2000, harry bought a gold ring for $590. which of the following functions f(x) can be used to represent the price of the ring x years after 2000?
f(x) = 590(1.35)x
f(x) = 590(0.65)x
f(x) = 35(0.41)x
f(x) = 35(1.59)x

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Answer from: 1044537

f(x) = 590(1.35)^x

Step-by-step explanation:

The exponential equation for growth in time period t is given by :-

f(x)=A(1+r)^t , where A is the initial value and r is the rate of growth in decimal.

Given : Rate of growth : r=35% = 0.35

Initial value : A = $590

Now, the functions f(x) can be used to represent the price of the ring x years after 2000 is given by :-

$f(x)=590(1+0.35)^x\\\\ f(x)=590(1.35)^x$

Answer from: Quest

"it's not the heat, it's the humidity". that's a partly valid phrase you may have heard in the summer, but it's actually both. the heat index, also known as the apparent temperature, is what the temperature feels like to the human body when relative humidity is combined with the air temperature. this has important considerations for the human body's comfort. when the body gets too hot, it begins to perspire or sweat to cool itself off. if the perspiration is not able to evaporate, the body cannot regulate its temperature. evaporation is a cooling process. when perspiration is evaporated off the body, it effectively reduces the body's temperature. when the atmospheric moisture content (i.e. relative humidity) is high, the rate of perspiration from the body decreases. in other words, the human body feels warmer in humid conditions. the opposite is true when the relative humidity decreases because the rate of perspiration increases. the body actually feels cooler in arid conditions. there is direct relationship between the air temperature and relative humidity and the heat index, meaning as the air temperature and relative humidity increase (decrease), the heat index increases (decreases).

step-by-step explanation:

75% of the temperatures are below what value? how do you know? 75% of the temperatures are above w

Answer from: Quest

$2^{2x+11}=3^{x-31}$

take the logarithm of both sides (the base of the log doesn't matter):

$\ln2^{2x+11}=\ln3^{x-31}$

apply the exponent property - this says that $\ln a^b=b\ln a$ :

$(2x+11)\ln2=(x-31)\ln3$

distribute the log terms on both sides:

$(2\ln2)x+11\ln2=(\ln3)x-31\ln3$

group like terms together:

$(2\ln2-\ln3)x=-11\ln2-31\ln3$

divide through both sides by the coefficient on $x$ :

$x=-\dfrac{11\ln2+31\ln3}{2\ln2-\ln3}$

you can do some additional rewriting here using the properties of the logarithm to simplify things if you like:

$x=-\dfrac{\ln2^{11}+\ln3^{31}}{\ln2^2-\ln3}$

$x=-\dfrac{\ln2^{11}3^{31}}{\ln\frac43}$

$x=-\log_{4/3}2^{11}3^{31}$

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