MHB Increase and decrease functions

AI Thread Summary
Increasing the value of 'a' in the function f(t)=a(1+r)t does not necessarily lead to an increase in the y-coordinate of the intersection point (y0) with the other graph. This is because the behavior of the function is influenced by the exponential growth rate, which can change the dynamics of the intersection. The graph's overall shape and the rate of increase depend on the parameters involved, not just the coefficient 'a'. Understanding these relationships is crucial for accurately predicting how changes in variables affect the graph. Analyzing the graph interactively can provide further insights into these dynamics.
jose1
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Hello
I have tried to resolve an exercise which is asking how the graph is modified according to the variables into the function. I would appreciate any help since accordin to my udnerstanding the function should increase

Please, follow below:
Suppose y0 is the y-coordinate of the point of intersection of the graphs below. Complete the statement below in order to correctly describe what happens to y0 if the value of a (in the blue graph of $$f(t)=a(1+r)t$$ below) is increased, and all other quantities remain the same.

If the value of a change, the function should be increased, but the answer is not. I would like to understand why?

View attachment 8577Regards,

Jose
 

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Let's examine a live graph:

[DESMOS]advanced: {"version":5,"graph":{"viewport":{"xmin":-5.365861436977749,"ymin":-1.3327205737064363,"xmax":17.212263563022272,"ymax":7.291467737981876}},"expressions":{"list":[{"type":"expression","id":"graph1","color":"#2d70b3","latex":"y=1.25^t","style":"SOLID"},{"type":"expression","id":"2","color":"#388c46","latex":"y=a\\cdot1.5^t","style":"SOLID"},{"type":"expression","id":"3","color":"#fa7e19","latex":"a=1","hidden":true,"sliderHardMin":true,"sliderHardMax":true,"sliderMin":"0","sliderMax":"5","sliderInterval":".01","style":"SOLID"}]}}[/DESMOS]

Move the slider, and look at how the intersection point changes when you change \(a\)...
 
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