am I right?

OK, heres what I'm trying to do,
I want to be able to keep track of activities along with companies.
So (I think) I need to have 2 MySQL tables. The first being a Company Table whose fields would be;
Company_Number (Primary Key),
Company_name,
Company_city,
Company_state,
Company_description,
Rationale,
Contact_name,
Contact_title,
Contact_phone,
Contact_email,
Medivas_pos.

The second (Activity) table would only have 5 fields;
Activity_number (Primary Key),
Company_Number (Foreign Key so each activity will have one company)
Activity_date,
Next_step.

I want to know if I have the logic figured out in making sure each activity would have a coresponding company attached to it, so I can perform a search by Company_name, as well as by Activity_date.
Thanks.

More info is always useful regarding the other fields, but yes, if you want to link an activity to a single company, that would be the way to do it.

Thanks for the input.
So, i'm trying to create the table, is the syntax and logic correct?
CREATE TABLE COMPANY
(
C_ID INT NOT NULL AUTO_INCREMENT,
C_NAME VARCHAR(20),
C_CITY VARCHAR(20),
C_STATE VARCHAR(10),
C_DESC TEXT,
RATIONALE TEXT,
contact_NAME VARCHAR(20),
contact_PHONE VARCHAR(15),
contact_EMAIL VARCHAR(20),
MEDIVAS VARCHAR(20),
PRIMARY KEY (C_ID)
);

CREATE TABLE ACTIVITY
(
A_ID INT NOT NULL AUTO_INCREMENT,
C_NUMBER INT NOT NULL,
A_DATE VARCHAR(20),
A_DESC TEXT,
FOREIGN_KEY (C_NUMBER)
REFRENCES COMPANY(C_ID),
PRIMARY KEY (A_ID)
);

Thank you, now i've been trying to seach 2 ways, by company name which works, I'm also trying to search by activity date which should daa from each tables The activity info and the coresponding company info...Can you help me!!
Thanks