Write the equation for an exponential function that is growth model with y-int: 3

Question

Please explain asap i have a final tomorow and this is the only question i dont get

Answer 1

When we have an exponential growth model, the independent variable x is the exponent and is positive.  Also, for the y-intercept to be 3, x has to be zero.

 

y = 3e^x

 

Let's check this model.  Plug in 0 into x.

 

y = 3e⁰

y = 3(1)

y = 3

 

The y-intercept is 3.  The model checks out.

Answer 2

Exponential functions for growth are sometimes given of the form:

 

G(t) = A*b^t, where b is the base of exponentiation or the growth factor of the model.

 

If we seek a y-intercept of 3, then the value of the function at time t=0 should be 3, so this equates to forcing A=3 for the model...thus:

 

G(t) = 3*b^t...without a second data point or information about the rate of growth, it is impossible to determine what the base or growth rate is....this is the general form for an exponential function with y-intercept 3.

 

Hope that helps!