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Anastasy [175]
2 years ago
6

Find a linear and an exponential equation that matches f(2)=12 and f(4)=48

Mathematics
1 answer:
Sergeeva-Olga [200]2 years ago
8 0

The exponential  equation that matches the coordinate is 3(2)^x while the linear equation is y = 6x

<h3>Exponential equation</h3>

The standard exponential equation is expressed as y= ab^x

where

a is the base

x is the exponent

Given the coordinates (2, 12) and (4, 48)

12 = ab^2

48 = ab^4

Find the ratio

4 = b^2

b = 2

Sice ab^2 = 12

4a = 12

a = 3

The exponential  equation that matches the coordinate is 3(2)^x

<u>For the linear equation</u>

The standard form is y = mx + b

m is the slope = 48-12/4-2
Slope = 12/2

Slope = 6

For the y-intercept

12 = 6(2) + b

b = 0

Hence the required linear equation is. y = 6x

Learn more on exponential and linear equation here: brainly.com/question/2456547

#SPJ1

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Here is the compound interest formula solved for years:
<span>Years = {log(total) -log(Principal)} ÷ log(1 + rate)
</span>Years = {log(800) - log(600)} <span>÷ log(1.025)
</span><span>Years = {2.903089987 -2.7781512504} / 0.010723865392
</span>Years = { <span> <span> <span> 0.1249387366 } / </span></span></span><span><span><span>0.010723865392
</span> </span> </span> Years = <span> <span> <span> 11.6505319708 </span> </span> </span>
That's how many years it takes for the $600 to become exactly $800.00
The question specifically asks how long for the money to be MORE than $800.00?

So, if we enter 800.01 into the equation, then the answer is
Years = {log(800.01) - log(600)} <span>÷ log(1.025)
</span><span>Years = {2.9030954156 -2.7781512504} / 0.010723865392
</span>Years = <span> <span> <span> 0.1249441652 </span> </span> </span> / 0.010723865392
<span> <span> <span> Years = 11.6510381875 </span> </span> </span>
<span><span> </span></span>












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3 years ago
A repair person charges $25 per hour plus and initial service charge of $30.
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