Exponential decay (which number line represents b in f(x)=ab^x?)

[tttete7]

I am stuck on this question because in my text book every other questions requires a graph I have never solved an exponential decay question having a number line. Thankyou for taking your time reading my question.

 

[Steven G]

What kind of numbers can b equal for an exponential decay (don't look at the number line yet)?
Can b <0? Can b>5? Think.

 

[Dr.Peterson]

View attachment 34736I am stuck on this question because in my text book every other questions requires a graph I have never solved an exponential decay question having a number line. Thankyou for taking your time reading my question.

Look in your textbook to see how they defined exponential decay, and whether they have ever shown an equation like $ab^x$. What do they say about it?

 

[tttete7]

Look in your textbook to see how they defined exponential decay, and whether they have ever shown an equation like $ab^x$. What do they say about it?

Well for example there is questions like : f(x) = 30(0.8)^(×)
The number outside the parentheses is "a" the number inside the parentheses is "b"
So we substitute x by 0 and the answer will become 30
Then we create a graph on the y- axis we point out the 30 and then we will check whether the slope is downward or upward since b<1 it's going downward toward the asymptote. That's how we solve it in the book the number line question is from the test practise section which I don't know when it's an exponential decay.

 

[tttete7]

What kind of numbers can b equal for an exponential decay (don't look at the number line yet)?
Can b <0? Can b>5? Think.

Umm b can be greater than 0 but less than 1
So we have
B#0 0<b<1
Wait so if we think about it like this then wouldn't the number lines leading to less than 0 be excluded then we have two more lines left the one that's between 0 and 1
One is its greater than or equal to sign so if we exclude that the one that remains is the number line with greater than 0 but less than 1 ... is thinking about it this way correct though?? TT

 

[Dr.Peterson]

Umm b can be greater than 0 but less than 1
So we have
B#0 0<b<1
Wait so if we think about it like this then wouldn't the number lines leading to less than 0 be excluded then we have two more lines left the one that's between 0 and 1
One is its greater than or equal to sign so if we exclude that the one that remains is the number line with greater than 0 but less than 1 ... is thinking about it this way correct though?? TT

You have the right inequality; the base isn't allowed to be negative or zero ever, and has to be less than 1 in order to represent decay (decrease).

Now, which number line graph represents that? I think you have the right answer, but you didn't say it!

 

[tttete7]

You have the right inequality; the base isn't allowed to be negative or zero ever, and has to be less than 1 in order to represent decay (decrease).

Now, which number line graph represents that? I think you have the right answer, but you didn't say it!

Ah now I get it! Thank youu

 

[Otis]

is thinking about it this way correct though?

I think so, tttete7. It's exactly how I'd approached the question.

With that type of multiple-choice scenario, a process of elimination (by applying critical thinking to each choice) works every time, for students who've learned (that is, who've practiced using and retained) definitions, conditions and properties. That's what the question was designed to test.

The base in any exponential function must be a positive number, so that eliminates all choices but (c).