Logarithms and exponential functions

The variables x and y satisfy the equation y=K(b^x). The graph of ln y against x is a st line passing thro the points (2.3,1.7) and (3.1,2.1) . Find the values of K and b correct to 2 dp
So when I did this I get the ans b =1.65 and K=0.05
But the text book says K=1.73

The variables x and y satisfy the equation y=K(b^x). The graph of ln y against x is a st line passing thro the points (2.3,1.7) and (3.1,2.1) . Find the values of K and b correct to 2 dp
So when I did this I get the ans b =1.65 and K=0.05
But the text book says K=1.73

Though your teacher probably hasn't told you, if you learn to use your calculator properly you will find that it can give you the value of k and b for data sets of equations of this type.

Can you give a hint of which submenu to go to? I'd have thought that finding the gradient and hence the intercept was the way. I was unaware that the calculator was able to shortcut all of this, and would welcome your insight.

Can you upload your working?
K being 0.05 (initial value) would be way too small

Can you give a hint of which submenu to go to? I'd have thought that finding the gradient and hence the intercept was the way. I was unaware that the calculator was able to shortcut all of this, and would welcome your insight.

Assuming you are using the Classwiz, it's Menu 6, then scroll down and option 2.

There's so much more that this calculator can do, that students don't get told about. Is it really asking too much that someone teaching A-level maths should know how to use the calculator, that most of his/her class are using, well, so that he/she can teach it to his/her students?

So I did ln y=ln k+ xlnb
Gradient= 0.5
So lnb =0.5
b=1.65 correct to 2dp
Y=1.6487x +c
2.1=1.6487×3.1+c
C=-3.01097
Lnk =-3.01097
K=0.05 correct to 2dp

When finding C you need
ln(b)
not b in the linear equation. Other than that, the method is fine.

So I do y= ln bX+c

You've written the correct equation
ln y=ln k+ xlnb
just plug the values in.

Assuming you are using the Classwiz, it's Menu 6, then scroll down and option 2.

There's so much more that this calculator can do, that students don't get told about. Is it really asking too much that someone teaching A-level maths should know how to use the calculator, that most of his/her class are using, well, so that he/she can teach it to his/her students?

DO NOT do this as you need to show working.

I agree about showing working out on this one. Was asking out of interest. But, it's always useful if people can check their answers, and hence correct themselves.

Assuming you are using the Classwiz, it's Menu 6, then scroll down and option 2.

There's so much more that this calculator can do, that students don't get told about. Is it really asking too much that someone teaching A-level maths should know how to use the calculator, that most of his/her class are using, well, so that he/she can teach it to his/her students?

Yes of course teachers show students but there are FAR more important things to focus on when teaching A level - developing problem solving skills, estimating answers, etc. etc. No-one should be a slave to their calculator which may not even been allowed at uni.

Over-reliance on a calculator also risks students writing down insufficient working and losing method marks.

Makes one wonder why manufacturers even bother adding useful features to mainstream calculators if hardly anyone is told how to use them. Perhaps we should resort to simple calculators and log books, like the good old days.

Makes one wonder why manufacturers even bother adding useful features to mainstream calculators if hardly anyone is told how to use them. Perhaps we should resort to simple calculators and log books, like the good old days.

Yes, you should know the underlying maths, but if there's a tool that can perform it quickly and efficiently for you then it's well worth knowing how to use it.