Question

Which equations represent exponential growth?

Which equations represent exponential decay?



Drag the choices into the boxes to complete the table.

Answer 1

Exponential Growth:

$A = 7000(1.0575)^{t}$

$P = 4500(1.04)^t$

$P = 45(2)^t$

Exponential Decay:

$V = 18,000(0.78)^t$

$P = 50(\frac{1}{2})^t$

$A = 9000(0.9)^t$

Although this may look tough, it's actually quite easy.

Basically, if the object of the exponent (the number before the exponent) is 1 or more, it is considered exponential growth.

If it's a fraction or decimal between 0 and 1, it's exponential decay.

Hope this helps! :)

Answer 2

The equations that represent exponential growth are:

$P = 4500(1.04)^t\\\\A = 7000(1.0575)^t\\\\P = 45(2)^t$

The equations that represent exponential decay are:

$V = 18000(0.78)^t\\\\P = 50(\frac{1}{2})^t\\\\A = 9000(0.9)^t$

An exponential function is of the form:

$y = a(b)^x$

If b < 1, the function represents an exponential decay

If b > 1, the function represents an exponential growth

Considering the exponential functions given:

Let us highlight the functions with b < 1

$V = 18000(0.78)^t\\\\P = 50(\frac{1}{2})^t\\\\A = 9000(0.9)^t$

The functions with the value of b > 1 are:

$P = 4500(1.04)^t\\\\A = 7000(1.0575)^t\\\\P = 45(2)^t$

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