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sesenic [268]
3 years ago
13

Write an exponential function y=ab^x whose graph passes through (1,6) and (3,54)

Mathematics
1 answer:
ehidna [41]3 years ago
7 0
y=ab^x\\\\(1;\ 6)\to x=1;\ y=6\\(3;\ 54)\to x=3;\ y=54\\\\\text{substitute the values of x and y to the equation}\\\\ \left\{\begin{array}{ccc}6=ab^1&\to&a=\dfrac{6}{b}^{(*)}\\54=ab^3\end{array}\right\\\\\text{substitute (*) to the second equation}\\\\54=\dfrac{6}{b}\cdot b^3\\\\54=6\cdot b^2\ \ \ \ |:6\\\\b=9\to b=\sqrt9\to b=3 \\\\\text{substitute the value of b to the (*)}\\\\a=\dfrac{6}{3}=2\\\\\text{Answer:}\ y=2\cdot3^x
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svlad2 [7]
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4 0
3 years ago
A parabola has vertex (2, 3) and contains the point (0, 0). find an equation that represents this parabola.
AfilCa [17]
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0  = a((-2)^2 + 3

4a = -3

a = -3/4

so our equation becomes  y =  (-3/4)(x - 2)^2 + 3




7 0
3 years ago
Consider the following expression: (1 + x)^n. A) Use the Binomial Theorem to find the first four terms of this polynomial. B) Wh
sergiy2304 [10]
Given:

The expression:  (1 + x)^n

The Binomial Theorem is used to predict the products of a binomial raised to a certain power, n, without multiplying the terms one by one. 

The following formula is used:

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we have (1 +x)^n,

where a = 1 
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let n = 4

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first term: 4*(1^(4-1))*x^1

Therefore, the first term is 4x. Do the same for the next three terms. 

2nd term: k =2 
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4th term: k = 4
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3 0
3 years ago
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Mariana [72]
We have to multiply those measurements to get the area of a living room
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5 0
3 years ago
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