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An exponential function in the form y = ab^x goes through the points (3, 10.125) and (6, 34.2). Find a to the

nearest integer and b to the nearest tenth, then find f (10) to the nearest integer.

User Lowtechsun
by
8.4k points

1 Answer

6 votes

Answer:


f(10) = 173

Explanation:

Given

Exponential Function


(x_1,y_1) = (3,10.125)


(x_2,y_2) = (6,34.2)

Required

Determine f(10)

We have that


y = ab^x

First, we need to solve for the values of a and b

For
(x_1,y_1) = (3,10.125)


10.125 = ab^3 --- (1)

For
(x_2,y_2) = (6,34.2)


34.2 = ab^6 ---- (2)

Divide (2) by (1)


(34.2)/(10.125) = (ab^6)/(ab^3)


(34.2)/(10.125) = (b^6)/(b^3)


3.38= b^(6-3)


3.38= b^(3)

Take cube root of both sides


b = \sqrt[3]{3.38}


b = 1.5

Substitute 1.5 for b in
10.125 = ab^3


10.125 = a * 1.5^3


10.125 = a * 3.375

Solve for a


a = (10.125)/(3.375)


a = 3

To solve for f(10).

This implies that x = 10

So, we have:


y = ab^x which becomes


y = 3 * 1.5^{10


y = 3 * 57.6650390625


y = 172.995117188


y = 173 -- approximated

Hence:


f(10) = 173

User Masrtis
by
8.0k points

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