Question

The graph of an exponential function has a y-intercept of 7 and contains the point (4,112). Construct the exponential function That describes the graph.

Answer 1

The exponential function that describes the graph is $y=7\cdot 2^x$

The standard form of an exponential function is expressed as $y=ab^x$

a is the y-intercept

(x, y) is the point on the graph

Given the following expression

a = 7

(x, y) = (4, 112)

Substitute the given values into the exponential equation

$y = ab^x\\112=7\cdot b^4\\b^4 = \frac{112}{7}\\b^4= 16\\b =\sqrt[4]{16}\\b = 2$

Get the required exponential equation

Recall that $y=ab^x$, hence the required equation will be $y=7\cdot 2^x$

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